jjmusicnotes is on the money with his suggestions to learn to play an instrument, and learn to read music etc. These things would help tremendously in your quest to develop the ability to write songs and express them to others musically.
However - it takes a great deal of time to learn an instrument and learn to write music and learn music theory. And from your question, it appears that you are already creating music and songs in your head that you feel are worth memorializing in some fashion. So I would like to give you some thoughts on how to start that process now, so you can get your ideas down and start writing songs WHILE you are learning to play an instrument, read and write music etc.
I am going to assume that since you can hear the melodies and arrangements "in your head", that you could also sing the melody (if not perfectly in key). If that is the case, your first course of action after you hear a song in your head, is to get to a recorder and sing what you hear to the best of your ability and save that file.
Many options include your cell phone, your computer (most have a built in mic and sound recorder software) or a simple digital tape recorder. If you get really serious, you could buy a multi track recorder so you can add harmony and bass lines on other tracks. All of these devices will allow you to save your recording as some type of sound file on your computer. There are many editing programs that will allow you to cut and paste sections to change certain parts, or add more parts to the end of each file. Some allow overdubbing as well, where you can record over a part you messed up or changed your mind about. There are free "audio cutter" and sound file conversion programs that you can download on the internet.
Step two, after getting the basic song concept recorded before you forget the brilliant melody and/or lyrics you were hearing in your head, start writing the lyrics. How to approach that would be another topic in itself, so I won't go into how to approach lyric writing in this answer.
You may or may not finish your ideas about all the lyrics, but after the first two steps, you will have a basic recording of your ideas for the musical arrangement and some ideas about the lyrics.
Step 3 would be to re-record your song after fleshing out the lyrics as far as you can get with them.
Now you have what you need to be able to share your ideas (what you were hearing in your head and tweaked after spending time working on it) with others. So now it's time for the magic!
Step 4 find a musician/songwriter (who has already spent the years necessary to learn to play an instrument and learn to write music and learned some basic music theory) to collaborate with. If you really do have some good ideas, you should be able to find a songwriter who is willing to co-write with you and help you finish and polish your ideas into finished songs. Then they can help you write the songs in music notation if that is something that is important to you - and/or record a demo of the song with as much instrumentation as desired. They will be willing to do this in exchange for co-writing credit. They will be adding the end result of your joint effort to their own catalog.
If after you share your demo with enough folks and start getting great feedback, you might consider going to a professional recording studio where the song can be professionally produced. If one of your co-written songs becomes a hit, you will get a portion of the writers royalties and can use that money for music lessons.
In reality, if your songs are good enough to be considered by a label or successful signed artist, you need to join a performance rights organization (PRO) such as BMI or ASCAP or SESAC (Google them) and execute a formal written co-write agreement with all co-writers. But that is another subject altogether as well.
One place to find co-writers/collaborators might be at a local songwriting organization in your community. In Georgia USA where I live, there is the Georgia Music Industry Association (GMIA) that meets twice per month. Also there are many chapters in the USA of the Nashville Songwriters Association International (NSAI) NSAI Website. There may be open mics in your community where song writers perform and you can meet them. Another idea is to contact some recording studios in your area that work with artists and songwriters who write the type of music you aspire to write, and ask them to connect you with some of their songwriting clients. Or the producer in the studio may help you finish your songs at the studio in exchange for the producer royalties and/or so you can hire them to record your demo once the song is finished.
So what I am saying is, if you are serious about being a songwriter, then follow jjmusicnotes advice and learn an instrument and learn music theory etc. But you don't have to wait until you can play an instrument to start writing songs.
I think you should start now with what you are able to do and with the help of an experienced musician. By the time you learn to play piano or guitar (two great instruments for songwriting) you will have quite a catalog of completed songs you have written.
Good luck - and be sure to post some of your finished songs on YouTube so I can hear them! If they are potential chart toppers, you can register your copyright in the USA on line at US Copyright Office