Independent yoga practice is what you make of it. It can be a soul-searching, meditative getaway or simply a good way to stretch out your muscles and relax.
There's almost no equipment necessary. I practice with a Gaiam yoga mat, purchased at Target for about $20. For months, I simply used a bath towel. The surface where you're practicing shouldn't be slippery so that you won't slide out of poses and injure yourself. If you have a carpeted floor, you may be able to do without the mat altogether.