The simplest and easiest screen recorder is Ocam (download from Cnet only, though). It's a 1 minute download, and it's a one button/hotkey click and record. I use it while playing (using it now). I turn it on whenever I log on. I do know some OS's and some PC's work better with other screen recorders, but to record a replay, it's perfect. The OBS for Twitch is a very unobtrusive recorder, also. Buy, a little more difficult to set up. Not sure about android.
Also, you can click "share" on the replay, and save the link (copy and paste to word pad or something for later viewing/recording).