There are two ways to control reflections
1) Absorption
2) Diffusion
Usually, your best results come from a combination of the two.
It's fairly easy to absorb sound in the upper and middle frequencies. It becomes very difficult to do so in the lower frequencies. A few bass traps in the corners of the room is usually the best way to absorb the most problem areas of low frequency sound. They're not cheap, and trying to save money with DIY products is rarely useful.
There are lots of options for middle and upper frequency absorbers, including DIY options. Some are cheaper than others. How well they work is all over the place.
Commercially made diffusers are very expensive. DIY versions can be made more cheaply although you need to know exactly what you're doing and there is a lot of time and effort involved.
A few shortcuts:
Thick carpeting (like shag) will absorb sound but only in the upper and mid frequencies. It won't do anything at all for lower frequencies. The floor is obviously a good place for it, but also try the walls.
Furniture can make good absorbers and diffusers. A big, stuffed EZ chair, or better yet - a sofa, will absorb a lot of sound, including some low frequency sound.
A full bookcase makes an excellent difussor. I've got two bookshelves in my home studio (about 5'x5' each) filled with books and they work great. They best place to locate them is on the wall opposite the sound source.
As a hobbyist musician with limited funds, my strategy has been to spend some money on a very basic commercial kit with a couple of bass traps, a half dozen absorbers and 2 - 4 diffusers (total cost maybe $500 - $1,000. Then supplement that with carpeting and furniture.
Some advise making do with improvised household materials like egg cartons and such. That's pretty much useless and a waste of your time.