Cheapest audible solution:
Good will/kindness solution:
- For an apartment, hotel room or space you don't own, you can try warming up and singing in the shower! You can also try vocalizing into a pillow or window curtains. However, don't practice in 'guarded stance'. A hunched over, too-careful posture and numb delivery could lead you into bad vocal technique, causing you to tighten up instead of loosen up!
- You can always practice in your car... but if you practice correctly you must be mindful of how you are singing. SO.... don't tailgate, stay away from other cars, or better yet... park and sing! Oh and don't let your posture slump.
- For your home, you might consider dedicating a space for playing/listening to/practicing music. In my home, my music room is located over my garage, and there is carpet on the floor. It really is a great situation for me and my students. So is, of course, the fact that I'm mostly working online with lessons, background vocals and production right now.
High end solutions
- Get some soundproofing or sound absorption materials for the room. While there are cheap ways to do this, don't line walls with flammable material.
- Construct a vocal booth
- Buy a vocal booth already made.
- Professionally design/build a soundproof room from scratch... or better yet, have an acoustical engineer or expert in architectural acoustics design it and build it for you.