EDIT: BIG THING. I assumed you were on monthlies and wanted to try dailies. If you have never used contacts before go to an optician for a check up again. They will show you how to put them in and take them out - this is very important you need a specialist to help you.

You also need to get the measurements for your eyes so that the contact lenses fit...
I'd suggest going into the opticians, at least initially, if after you've had them for a while and are happy with them you want to simply order online then that's up to you but you are better off getting them done properly to start with. If you've got astigmatism in one eye then that changes the prescription for instance. Any optician should offer free aftercare with the lenses you buy so you'll have at least one or two check ups to ensure there are no problems.