There is really no standard formula for writing songs, which is both good and bad. Bad - because you cannot simply plug in a set of chords into a transformation and have guaranteed results. Good - because the only thing that matters is whether it sounds good to you.
However, there are some tricks that work and I'll try to briefly outline them here. Be prepared to experiment a lot, because that's the only way you can find out what works for you.
The first thing you're going to want to consider is the form of your song - what parts make it up and how they're supposed to fit together. If you have lyrics that you are writing the music to, take a moment to read them and think about how your music will help them best bring their meaning across.
Consider this most basic song form:
verse - CHORUS - verse - CHORUS - verse - DOUBLE CHORUS
The chorus is meant to be the most energetic and singable part of the song - the one that should stand out most (hence the CAPS). Therefore, you're going to want to put your best chord progression there - the one you could play over and over again.
The verse is probably going to be somewhat less energetic, more conversational. You want it to provide contrast, but at the same time to set up the chorus that is to come. For the verse, you'll want to find a progression that sounds good with your chorus and - ideally - one that has a good lead into the chorus.
Finding your progressions
The cheat sheet you've linked has its problems, but it is an okay place to start. Take some time to play through the progressions they've given as examples; try as many keys as you can manage; listen to how the chords sound together and what changes really speak to you.
Remember to vary your playing style as much as you can: try playing fast and playing slow. Let the chords ring out or go for a more rhythmic approach - or even give the progression room to breathe by introducing rests between the chords.
Want more progressions to experiment with? Play them backwards! Or maybe start in the middle. Hack these progressions up an glue them back together to see how that is going to sound. In a lot of cases, the chords are going to sound good together no matter what order you play them in - and if not: you've learned something useful.
You really want to spend a lot of time playing around with these, to get a good idea of what the sounds you can get from various chord changes.
Choosing a chorus for your verse (and vice versa)
Right now, you've found that a Em to D change sounds good, but none of the progressions you've tried seem to do the job. What to do?
Simply put: assume your chorus is going to start from D and take it from there. Look through the chart of keys and see where the D chord appears: your choices are G major, D major and A major.
Your next step should be to see what progressions are available with the D chord in each of these keys. In D major, the most obvious choice would be:
I-IV-V - D - G - A
but don't neglect the opportunity of tweaking the order a bit:
I-V-IV - D - A - G (classical harmony buffs will gasp in horror at V-IV, but we needn't care)
In G major (the relative major to your E minor verse) we have:
I-IV-V - G - C - D
The D chord is at the end, but who says we have to start at the beginning:
V-I-IV - D - G - C
This is only the tip of the iceberg, of course, and you should try out any progression you can come up with - either by plugging a key into one of the progressions listed (remember, you have three to choose from here: A major, G major, D major) or by changing the order of chords around to have D be your starting chord.
While you're experimenting, keep in mind that you want to find something that not only works well coming in (verse to chorus) but also going out (chorus to verse).
Chords that work well together
Here are some quick-and-dirty rules of thumb that can help you spot chords changes that work well (although they may not always be appropriate in your setting):
Changing to a chord one step higher is going to sound good - this works both for half-steps (e.g. B-C) and whole steps (C-D).
Changing from a I chord to a V chord is going to sound good.
Changing from a V chord to a I chord is going to sound good.
You can see this in the basic I-IV-V progression:
In C major, the I and IV are C and F. In F major, C is V and F is I (a V chord moves to a I chord).
In C major, the IV and V are F and G. They are one (whole) step apart and the change moves up.
In C major, the V and I are G and C. It is a V to I move and it sounds good.
And, indeed, a I-IV-V repeating progression sounds pretty damn fine.
When looking to change from verse to chorus or from chorus to verse - look to see what chord you would need to get where you're going.
Here, you've found that Em to D sounds good. It is a change going one whole step up. To use the same idea to lead back into the verse, you would need to make an A to Bm move, so the last chord of your chorus would have to be an A.
It so happens, that you can get this by using the I-IV-V (D-G-A) progression from D major.
Note: For the purpose of this quick-and-dirty analysis, it doesn't matter if the actual chords are minor or major - the changes will work either way, so you can try substituting minor for major and vice versa.
Breaking things up
Say you have a verse you really like and a chorus that ain't half bad either, but sadly they don't fit together very well. You already know (from what was written previously) what chords would work well together in the transition, but unfortunately these aren't the chords you're already using - and like.
What to do in this situation? Add a bridge.
A bridge is a small section of music between two major parts. Typical applications include:
verse - bridge - CHORUS
verse - CHORUS - bridge
verse - bridge - CHORUS - bridge - next verse
Because the bridge doesn't really need to stand alone, like the verse and chorus, you can use it as a kind of "glue" to stick two sections together. Simply make sure that the first chord of the bridge is one that sounds good coming in from the verse and that the last chord is one that sounds good going into the chorus. Even one chord held over a couple of bars might do the trick, if it happens to be that single chord you need to make the transition.
Don't forget dynamics
We sometimes forget that you can get away with a single progression driving away throughout the whole of the song - provided we make things interesting.
Take Smells Like Teen Spirit, by Nirvana. It's not a song I am particularly fond of, but it illustrates how you can use the same progression for both the verse and the chorus, if you vary the dynamics.
The chorus is big, loud, slashing chords. The verse, on the other hand, dials back the drums and has only the bass carry the chord changes, while the guitar plays a simple, two-note lead. All of a sudden, there is variety and the song works (if popularity is anything to judge by).
Sometimes, you don't need another progression - perhaps you only need to change the way you play it.
Quick and dirty trick: transpose the lot
One easy way to add variety is to take a chord progression you are already using - for your verse, say - and transpose the whole thing, lock, stock and barrel. For example, a I-IV-V verse in C major (C-F-G) might be transposed to D major (D-G-A).
Use this as a bridge, or pre-chorus, and then transpose right back to the original key for the chorus.
This is, essentially, how Metallica's Enter Sandman is built.
Transposing up a whole step - C major to D major, for example - works really well, but you can also try transposing four (C major to F major) or five (C major to G major) steps.
I encourage you to keep notes of progressions, ideas and chord changes that you like as you are experimenting and writing. When you learn a song, take a moment to write out the form and the progressions in Roman numeral notation. Look for recurring patterns, such as some I have outlined above. The next time you're stuck, you'll have a pretty good idea of where to begin looking, at least.
For all I've written, at the end of the day we still often find ourselves just sitting down and trying different changes, because what we've got so far simply isn't what we are looking for. That's part and parcel of being a songwriter, so don't worry if you get stuck sometimes. We all do.
I hope this will help you get a better understanding of how to find the right progressions for your songs and how to fit them together.