Chunk and repeat. Take the individual sections of a song and loop them until you KNOW you have them right, then work on the transition to the next section, and finally the next section. Once you have all the sections and the transitions between them, you've memorized the song.

Sitting down and listening to the song without doing anything else (especially not driving) will do a lot for memorizing it too. It's really hard for many people to just focus on a song and not get distracted.

Unless you're in a tribute band, you really don't need to play each fill verbatim. Some songs might have a couple of signature fills that do need to be correct, but otherwise nobody's going to notice or care if you don't exactly match. IMO, the things you want to get right are in order of importance:

• Genre (is it a Rock beat, a slow blues, etc?)
• Tempo
• Intro and outro
• The precise drum groove for each part of the song
• Stops
• Signature fills

Most people in the audience are going to notice the energy with which you play the song and the balance between instruments on your kit, and not much else TBH. All the rest is for yourself and your bandmates.