What would be a good method to learn musical notation, especially how to read the pitches of the notes fast enough to play them on your instrument (sight read)?
It's great that you want to learn! A key part of experiencing music, in my opinion, is being able to read it! (Again, my opinion; many people will probably disagree in comments below.)
My suggestion is that you go about learning to read music the way you would go about learning anything; lessons are nice but not absolutely necessary (though if you are still in grade school, music theory or other music elective classes would be helpful [depending on the school and how much you are willing to apply yourself/pay attention]); YouTube should have a myriad of view-hungry teachers and various styles of presenting the information. For something a little more professional (but still not too pricey), a service like Google Helpouts should be able to answer those random questions that you want super-interactive answers to....and of course, we at music.sx are always willing to enlighten you whenever you think you might need it :)
Books are an excellent, especially since notation isn't one of those things that has changed a whole lot over the past several decades. And any website devoted to music theory info is worth a look or two! Here are some I've found (listed in no particular order) [though most of these go farther than just reading music]:
Keep in mind that using what you learn is key to really processing and understanding (and remembering!) it all. Writing your own melodies or transcribing (trying to write in musical notation) existing melodies is a great way to exercise your new knowledge; some great free notation tools (there are many unfree ones, Finale and Sibelius being the primary products) that will even play back what you've written for you. Musescore is what I use when I'm not using Finale (which is usually when I'm on my Ubuntu laptop --yay for multi-platform sofware), but if you're reluctant to do any downloading/installing, Noteflight is one browser-based notation application that I know of (I've never used it myself, but it's been highly acclaimed). And, as the genius Wheat Williams has suggested, you can also follow along with others' work as well. Both MuseScore and Noteflight (I believe) have places where you can upload your own scores and listen to others', which is a great (and fun) way to share music!
I would recommend having some sort of keyboard instrument (piano recommended) at hand to mess around on while you're trying to figure out what you're reading/hearing. (Notice that I didn't say "learning to play piano"... You can learn to play whatever you want [and learning to play something is recommended, because music. :D ], but keyboard instruments are undoubtedly the easiest for visualization.)
Well, this seems fairly obvious, but the best thing you could do would be to learn to read music while learning an instrument. This way, you are developing more neurological connections in your brain simultaneously.
Never think that music is about being fast; it is about being consistent and exact.
A helpful method, assuming you know enough music notation to follow a melody, is to try and follow the sheet music of a piece while you are listening to a recording of it. This presupposes that you can find a recording and also some printed sheet music that is a fairly accurate transcription of the particular arrangement you are listening to.
Get yourself a good theory teacher and start counting notes. There is no simple way about it. You start on the G where the treble clef gets its name from (Second line from bottom on the staff) and you count upwards and downwards.
You have the Notes A-B-C-D-E-F-G.
If you go up on the staff you count forwards on the above graph and when you go down on the staff you count backwards. Counting backwards is a bit tricky at first. You are usually not taught how to count the alphabet backwards in school.
We have notes in spaces and on lines. The G we start counting from is on the second line from bottom. SO for instance if we have a note below the G we have an F. If we have a note above G we have A.
For the bass clef you start counting on a different spot. You begin counting on the line second from TOP this time which is an F. The two dots between the second line from top indicate where you should start counting.
Again the note above F is G. The note below F is E.
Middle C on the Treble Clef is on the the first ledger line below the staff while middle C on the Bass Cleff is on the first ledger line above the staff. When you start writing notes on different cleffs you determine where the given note is in relation to middle C and then find where that note is on the other cleff.
There is no easy way about it. You count notes again and again until one day you now there names of by heart. It is one of the reasons why music theory is such an integral part of music. This is one of the first things you are taught in music theory.
Another answer in addition to all the other perfectly good ones:
First, get a good set of flash cards. These are the ones I have always used with my students: http://www.amazon.com/Flashcards-General-Music-Jane-Bastien/dp/B000E3WW7M/ref=pd_sim_b_1 . Then, use these mnemonics, which have been around for more than 100 years:
Treble clef lines, bottom to top: EGBDF Every Good Boy Does Fine
That will get you started with the pitch values. Get all those so you're quick at them on the flash cards. Then go through each card, playing the note on the keyboard, until you do it easily. Then start adding more notes above and below the clefs.
You also need to learn the duration values, which are also on these flash cards. Start with whole, half, and quarter notes and rests. (Note that I mentioned rests!) Add in eighth and sixteenth. Then understand what a dot does to a note (multiplies its duration by 1.5, if you're arithmetically inclined), and then work in 32nd, 64th and 128th notes when you thoroughly understand these.
At that point, you're like a chess player who has learned the moves. A beginner, in other words. :) Keep that beginner's mind, no matter how advanced you get.
Finally, I once read someone say that the only way to learn sight reading is to sight read. I've found that to be very true in my experience. Find books full of simple music (hymns are a good starting place) and keep at it. Make sure that you use music that is fully written out; fake books and the like are a more advanced skill.
Notation encodes both rhythm and pitch. Both can be learned separately, and this allows you to become familiar with either aspect without being distracted by the other.
There are a couple of reasons why it makes sense, at least while you're still learning notation, to separate these aspects. For a vast majority of western music, both rhythm and pitch move in patterns. Learning these patterns simplifies reading music a lot. And the patterns for rhythm and pitch organization are orthogonal and in practice completely independent. So, you can learn them independently too.
At a very high level, rhythmic patterns are implied by time signature which a conventionally associated pattern of strong and weak beats. For instance, of you have a 4/4 measure, the 1 and the 3 would be typically relatively emphasized, and the 2 and the 4 relatively weak counts. And if that 4/4 would be further divided into 8th notes, counted as "1 and 2 and 3 and 4 and", if it would yet be further divided into 16th notes, you'd count it as "1-uh-and-uh-2-uh-and-uh-and-uh-3-uh-and-uh-4-uh-and-uh". This counting schemes are really just a way to let you mentally count out rhythmic patterns, which you can then practice, practice, and practice some more until basic rhythmic motivs in various time signatures are so familiar that you don't need to think about it anymore when you're reading them on the spot.
Again, at a very high level, pitch is typically organized in scales, and are typically denoted by the key signature. The key signature limits the set of notes that are most typically used throughout a piece (or section of a piece). By practicing scales, you develop the skill to hit those notes on the instrument you happen to play, again until they are so familiar that they come naturally and virtually without thinking.
Now, training these things separately are simply devices to help you focus and not get distracted by either aspect while learning. You can and should also practice to play or sing examples that combine pitch and rhythm, but by preceding this with separate study of rhythm and pitch, you will notice that you can "parse" real music examples much quicker. This automatation is what eventually will need to develop in order to be able to sight read.
A great way to get started is by taking a solfege course. (http://en.wikipedia.org/wiki/Solf%C3%A8ge). This allows you to focus on notation without being distracted by the specific peculiarities of an instrument at all. One could argue that the instrument is the voice in this case, but there is still a difference since solfege is not really about learning how to sing, it is simply about learning how to internalize music. And since the voice is so directly linked to your body, it is a good way to help you form a mental impression of the notated music.
It is important to realize that this does not substitute learning your instrument - these are simply devices that learn you the skills that help you parse music notation, and to learn how to automate that to the extent that you don't need to think so much about it at the time of performance.
"What would be a good method to learn musical notation, especially how to read the pitches of the notes fast enough to play them on your instrument (sight read)?"
That's like asking "what would be a good method to learn the alphabet, especially how to read the letters of the words fast enough to recite poetry?" The process of playing notes on an instrument is only loosely connected with reading or knowing or naming individual notes. Learning musical notation is a good dry start before learning any particular instrument.
Knowing how to play an instrument is going to make acquiring musical notation easier, too. Marrying both, playing an instrument from notes, is going to take a whole lot of time and practice, regardless whether you start with one, or the other, or learn both at the same time.
Doing both at the same time is likely the fastest way, but you can expect the abstract "music notation" angle to suffer a bit from it. For example, when learning the violin, whenever somebody asks you what a particular note is named, you'll count off the notes from the empty strings, like "that's two notes above a, should be a c".