Start off by purchasing some Studio Foam. You might have seen this used by some of the hottest musicians and producers. By using Studio Foam you will ensure that your vocals sound the best they can sound. This means crystal clear clarity which makes for a fuller mix. Studio foam will most likely come in square pads or rectangle wedges, therefore making it easier to work with on corners of the room. Start by doing the "Hand Clap" test to determine which part of the room you must insulate.
Put some Studio Foam glue on the back of one of the pieces of foam and press firmly against the wall. It's best to press and hold the pad in the place for about 10 seconds to make sure the glue actually sticks to the wall. Do this around all the sensitive parts of the room that have excess echo.
When using Studio Foam it's also best to place a couple of pads or wedges on the ceiling. A lot of producers choose not to pad the ceiling because they want a wider "backdrop" for the vocals, but I recommend placing a couple pads just to balance out the room. Once all pads are in place, go over them by placing 1 or 2 small nails in the corners just to ensure they don't fall.
Once done with pads, do a sound test by yelling loud to see where the echo is. If you hear lots of echo that means more pads. However; if you yell and hear little to no echo, then you've done a good job! You can now begin recording in your soundproof room!