Take two courses. Get amazing grades. Write an awesome letter, basically exactly what Star said.
You will want to include
- what went wrong
- what steps you took to address this
- what you would do differently next time
- why this will not happen again
- why they should give you a second chance
- any documentation that can verify any of the above
Excuses you will want to avoid:
- being away from home
- deaths in your non-immediate family
... just because they see it all the time. I mean, if it's true then it's true, but I suspect it won't help your case much. Also, if any of these were your excuse for doing poorly, you may want to take that year off... I don't say this with judgment, I say this from a place of experience. Not everyone is ready for this kind of pressure in first year, and part of this university thing is being able to withstand a lot of these things that often trip up first years.
You will want to get this letter proofread, and be prepared to write and rewrite a few times. Each time you rewrite it, your letter will be better.
If you do not get back in:
- don't panic
- keep learning
- grow as a person
- try again next year