I first learned my guitar by borrowing my cousin's and playing random stuff on it. Then I went online, and searched out tabs for songs that I liked, and practiced/played them to death.

One good starting thing, which most beginners hate, is technique practice. It's absolutely crucial for the guitar, especially since there's a lot more expressiveness that you can pull off, the more techniques you know. (E.g. vibrato, bending, bending + vibrato, etc). But since you're a musician yourself (piano + trumpet) I'm pretty sure practice isn't something that comes hard for you.

Like the above Anonymous, I say start off with chords. Memorize the finger forms. Learn the basic major + minor chords, before you delve into the other weird stuff (e.g. sevenths, thirteenths, diminished, etc.)

Absolutely develop your picking technique. There are two:

1) Fingerstyle.
2) With a pick/plectrum.

It's easier to go for the second one. Also, picking technique is generally divided into two types: alternate picking, and directional picking.

Alternate: Constant up-down picking motion.
Directional: Picking motion depends on where you're going: If you're going to the next string which is above the current one, you pick upwards. (To distinguish this from alternate picking: if the next string is above, but the next picking motion should be downwards, then you have to pick downwards.)

Picking techniques are absolutely crucial to master. It's not like the piano, where pressing one key is sufficient to make one note sound off. Plus picking determines the dynamics of your playing. Volume and ferocity is in your picking hand. With practice, you can do cool stuff like palm muting and sweeping techniques. (For more info, Google them.)

Hope I've helped. Feel free to ask more!