14.09.2013

Today is saturday. Today i dont work and go to university on one lessons only. The wether is good. I have go to shop for a food. And today i have learn some songs at the guitar.

And now it's my version of your text:

It's saturday. I don't need to go to work and I just have to stop by at the university for one lesson only. The weather is good. I need to go to the store and buy something to eat.

And today I've already managed to learn some songs in the guitar

14.09.2013

Today is Saturday. Today I don't have to work and only have to go to university for one lessons (better to use lecture or seminar for university lessons) only. The weather is good. I have go to the shop for a food. And today this morning I have learned/learnt some songs at on the guitar.

Great job - only a few small mistakes. Why not try putting some of the shorter sentences together to make more complex ones?
It's Saturday! I don't have to work today and only need to go to university for one lecture. The weather is great. This morning I was able to learn some new songs on my guitar and later I'll go food shopping. Enjoy your weekend!
Obviously this is just one way you could write it. Next time, try to turn some of those full stops into commas of conjunctions. Keep it up :) 

14.09.2013

Today is saturday. Today i dont go work and I'm going to university for one lessons only. The weather is good. I have to go to shop for food. And today i have learn some songs at the guitar.

good job. :)