I have a lenovo h50-55 90bg003jus desktop I've been wanting to get a better graphics card because I can't really play much games on it?

I don't know what will work and what won't I don't know what to get or how to start looking.

Your Lenovo tower has a AMD R7 inside the CPU chip for video. You will have to get higher than that for better results. There's a PCIe 16X slot for a card but I can't find a power rating for the supply unit. Take off the side and read the PSU label to find what level it will put out. Do a search for a card that has that recommended level or less. Or replace the power supply with a bigger one.