One of the biggest things you'll need is a good credit score. This can be built up by paying off credit cards, rent, care payments, etc. quickly. Since you haven't rented an apartment before, you may need to find a co-signer to sign your lease with you. This means that they will be responsible for making payments if you aren't able to make them. You may want to ask a family member or close friend that you trust to help with this.
Many apartment complexes require renter's insurance, which will protect your belongings in case of fire, flooding, theft, etc. I would go ahead and start looking into good deals on renter's insurance.
When looking for an apartment, keep in mind the neighborhood and area. I would definitely suggest not subleasing off of Craigslist; there are many stories of things that have gone wrong by using that method. Talk to people who live in the apartment complex to see what things are truly like.
Finally, make sure you read through every word of the lease so that you fully understand your obligations. Best of luck to you!