You are in that in-between stage - not completely built up yet credit wise - but not just out of high school either.
There are a number of excellent things you can do.
1. Have a credit card (even if it is a secured one that you have to deposit money into to get) and charge up a small amount each month of your money expenses (like food) and then diligently pay it off every month.
2. If you can pay your auto insurance monthly as well and be on time every month that is also a good thing.
3. Do you have utility bills you pay regularly?
4. Do not be late on anything.
5. Build up savings.
Approach everyone you have had responsible dealings with (past landlords, employers, bankers, ect.) and built a strong reference list to provide with your application.
It is a tight rental market - you may need to find a roommate that has stronger credit and have them be the main signer on the lease. You could also stop by property management companies in person and introduce yourself - personally hand deliver the reference letters and ask them to take the time to go through and check your references and keep you in mind when something comes up (a box of chocolates along with that might encourage them to take the time to do so) ;)
Driving around and calling off for rent signs is often an untapped market as well - look in condo and townhome areas for the price range you are trying to stay in. One of my investor clients only found renters putting up a sign in the yard and that was all they had to do since they received multiple calls within days.
Hope this helps! I have some resources of other companies that are more than willing to give you much more in-depth advise to build your credit as well at no charge. Let me know if you'd like their names.
I'm assuming that you are employed or have a regular income coming in
At some point, you will want to spend a Saturday looking at the credit building advice. Ask TransUnion or another credit tracking company for a copy of your credit history. Is there a car loan that you paid off? That will help.
They used to hand out credit cards like candy to students.
In Longmont, Elevations Credit Union will allow you to set up a debit card account that becomes a credit card account, if you keep a positive balance. The required balance is something like $1,000. After six months, you've got credit you can use. You might want to wear a business appropriate outfit and go apply at the branch on south Hover Street (behind the Starbucks) across from Twin Peaks Mall.
I know researching this stuff is work. But you can do it. Good luck to you, young one.