While the other solution authors are correct that this shouldn't be too hard to get, given that just about every level have over 100 coins, I thought a bit more specific guidance might be appropriate.
I suggest getting this in the first stage, Green Hill Zone Act 1. First of all, be sure to grab the flashing bonus coin box at the very start of the level (which will give you ten coins), then as you move forward grab as many coins as you can, stopping to save every once in a while in case you accidentally die.
Then not too far into the level, you reach a yellow spring that bounced you onto a crumbling cliff. One you grab those coins on the cliff, go BACK and fall down to the ledge below. Keep going straight under the cliff and after jumping over some spikes, you'll find three more of those bonus coin boxes worth a total of 30 coins.
From there on just keep going forward til the end of the level and grab as many coins as you can. It should be a cinch to get 100 from there.