Getting kitted out
It's best to have a special set of clothes that you only use for yoga practice. These should allow complete freedom of movement and preferably be made of natural fibre, cotton is best. Some people practice in shorts, some in dance clothes, some in track suits, and of course, some in specialised (and usually overpriced) yoga clothes. All of these work fine, as long as they are comfortable and clean.
A non slip yoga mat is strongly recommended for Asana practice. It's worth paying more for a good quality, hard wearing one, as some of the cheap ones don't last very long!
For sitting practice, a blanket folded on the floor is enough for some die hards, but most people will also want a meditation cushion, or a zafu, or a meditation stool, or a yoga block, or even all of them. Any yoga online shop will be happy to sell you these, just shop.
Some practitioners prefer to sit on a chair, a good and inexpensive option for people with stiff hips.