This would be better conveyed via a video, but I've been too lazy to do that yet.
Overview
I'm a drummer, and I've struggled with timing. I don't mean the kind of timing where I'm slightly off beat when returning from a fill. I mean when I transition from one groove to another, and I'm way off. Or I'm playing the same groove for a minute. How do I not speed-up or slow-down? How do I know that I'm keeping the same time after a transition? I would have no idea. A mistake I made was to try and remember how fast my hand was going on the hi-hat, and try to replicate that speed on the ride (if that's what the song did). That just doesn't work. First, what feels fast one day, may not feel fast the next. Fast is subjective. Second, I may be playing eighth notes on the hi-hat, but then I switch to quarters on the ride. That simply doesn't work while trying to maintain the same speed. So what did I do?
Tip #1
Use the other instruments as a metronome, including vocals. We can all play along to a metronome, right? Well, your other band members are providing a metronome for you, and you may not realize it. Some songs are more obvious than others.
Examples
Should I Stay or Should I Go - The Clash
The guitar starts the song, and gives you: "and two and three and four and one." The guitar literally gives you that count. Play to it. Sing the guitar in your head, while you play, as: "and two and three and four and one."
Lonely Is The Night - Billy Squier
The vocals give you: "somebody’s watching you, baby," use, "1 and 2 and 3e and 4 and." The "3e" lines up with "watching you." As the singer is singing that part, sing "1 and 2 and 3e and 4 and." Like, literally sing that to yourself, or mildly out loud, while you play.
The Joker - Steve Miller Band
The bass gives you: "one and two and-uh-three and four, one and two and-uh-three-e-and-uh-four-e-and-uh." That happens over and over again. That's your metronome. LISTEN to it and play along to it. Let it guide you. Try to make the drums match the bass.
Take It Easy - The Eagles
"Well I'm a runnin' down the road..." lines-up perfectly: "Well I'm a one and two and three and four and..." Sing the lyrics as, "one and two and..." right over the real lyrics.
You'll realize more and more opportunities for this approach once you start applying it.
Tip #2
Sing the melody as counting, like: "one and two and three and four and."
Examples
867-5309/Jenny - Tommy Tutone
This could also fall in the category above. While you play, try singing 8675309 as "one and two and three and four and three oooo ni-ine." At any point in the song, you can sing like this, even when that's not what is being sung at the time.
What I like About You - The Romantics
The guitar/melody gives you: "1, 2, 3, 4." Listen to it and feel it. Play along while singing the melody. You can sing: "1, 2, 3, 4" while the guitar is playing it.
Tip #3
Use the 210 approach on the metronome.
There are some songs that aren't helpful as far as other instruments. Perhaps the drums are on their own for a bit. Or perhaps the guitar is just riding out a power chord for a while.
Set your metronome to play three bars. For the first bar, let the click happen on one and two. There should be silence on three and four. For the second bar, only the one should click. For the third bar, there should be no clicks. Let those three bars repeat. Play along to it. Get used to having to keep time on your own, and coming back in on time. Don't be robotic though. Try to keep some kind of melody in your head to guide you.
If your metronome doesn't do this. Get one that does. I use Metronomics HD.
Examples
Shakin' - Eddie Money
This song starts out on the drums. It's a tom groove that's pretty cool. Then there is the transition to a normal, easy beat. Keeping that time wasn't easy for me. I used to play 8th notes on the hi-hat only because I was also doing it on the floor tom. But I wanted to play quarters on the hi-hat, after the tom groove. There are no other instruments to guide me here. So I set my metronome to 113 BPM (to match the song) and I did the tom groove to it, over and over again. Then I did the simple beat for a while. Then, and this is the important part, I played the transition between the two, over and over again, for like 20 minutes straight. It's rough at first. And 5 minutes is a long time for this, let alone 20. But after 20 minutes, the tempo ends up burning into your memory, and you can do it.
This approach is also useful for double time. For example, Lonely Is the Night, and Should I Stay or Should I Go, each have double-time pieces. That is, where the snare was on 2 and 4 earlier, it's now on 1, 2, 3, and 4. Just like Shakin', turn on the metronome and practice the transition for long periods of time. It will sink in. You can also sing the melody during these parts.
The 210 approach also helped me with Born to Be Wild, by Steppenwolf. During the chorus, 16th notes are played on the toms, with crashes in there. 20-30 minutes of 210 helps get this right.
Hopefully this helps. If you have any extra tips, feel free to comment.