I just started wearing contacts, on week 4 i think of my trial. I've tried a couple of different monthlys, and am testing dailys at the moment.
You will need to go to an optician to get your eyes tested and measured (different to glasses prescription usually ), lenses fitted to your eyes (checked to make sure they are ok) and then they will let you try them for a week or so. Come back try other ones etc till you get a nice comfy one. Once you have your prescription you can go anywhere you like to get lenses etc. They'll also show you how to clean, handle, store put in and remove your lenses, which may be a problem for some people.
I must say I was skeptical at first, but wearing contacts is absolutely freaking amazing. The dailys are even more comfortable - totally can't feel anything. The most annoying thing about it is forgetting you aren't wearing glasses. Like how you do stupid hand movements when scratching your face etc to not knock your specs etc