The cheapest most cost efficient way is to turn a closet into a vocal booth, get acoustic foam and place it in your closet. It will work great and won't bother neighbors.
This is as good as it gets. I would have provided a pic of mine but I've filled it with clutter again.
A closet with foam and some sort of easily removable (from the inside) draft proofing) would be a bonus if you have noise issues outside. Add a drummer's stool and a straight mic stand with small base and you're off.
Also, break the bank and buy yourself an inexpensive battery operate light with a sticky pad to attach to the wall. You should get one for around £10/$15. Even a nice flourescent LED one. Hell, I'm even planning on building a little shelf for singers to have a glass of lemonade in between takes. Well that was the plan until the condenser picked up the fizzing...lol