Figure out what subgenre of vaporwave you want to do. There isn't a real vaporwave, it's more a couple of sub-genre one derives from another. You can find out more about each one by researching Vaporwave subreddit wiki.
Browse the internet for some 70's, 80's, 90's music. This is the most common music sampled in vaporwave. One thing to note is vaporwave is highly, if not fully, sampled. New wave music based heavily with synthesizer noises and smooth saxophone leads seem to be the favorite for sampling from.
Take the song into your favorite DAW. DAW stands for Digital Audio Workstation (I.E. FL Studio, Ableton Live, Logic, Cubase, Pro Tools, Sonar, Reason, etc.) and is the common tool today for making music. Once you have imported the song into your DAW, you want to do your best to match the BPM of your project and sync them together so it's easier to slice apart into samples/loops.
Make it slow. The most common rate of slowing down music to make it vaporwave is anywhere from 20-60 BPM slower than the original, and if it has vocals, make sure that it's slow enough to where the vocals sound eerie and almost nightmarish, and let that be your reference to how much to slow your track down.
Select your favorite part of the track and cut it.
Experiment. Try to repeat some parts, add effects, delete the parts than you hate, until it sounds good for you.
Save the file in any format you want. Flac is the best, but it's a really heavy format. Commonly, the most used is mp3 or mp4 if you want to upload it on YouTube.