It's very easy. I went with Fidelity and signed up for a Roth. You fill out some forms (online even if you want, which is what I did) and can either mail in a check or have money wired from your bank into your account.
I had $3,500 wired in and invested in a widely-diversified Vanguard mutual fund. Fidelity charged me a $75 fee to buy as many shares as I could afford. They are synced with Quicken if you use that, and have online account accessibility.
Very easy to do. If I managed to do it, you definitely can without issue.
If you don't want to put in the minimum deposit of $2,000 (I think it's around there) they have the option of setting up a Roth that automatically takes X amount of dollars (lowest is $200) out of your checking or savings each month. With this kind of setup (with Fidelity as least) you have to fill out paperwork and mail it in, no online signup.
Feel free to IM or email me if you have any questions.