When you forget your anniversary, you'll break somebody's heart a little bit. Your first step is mending that, but not before you sit back and bear the brunt of their anger.
So take it. If your spouse is angry, let them be angry and don't bicker back. Give them as long as they need to vent their hurt.
Now it's your turn to talk. Sit down with them, take their hand, and really, seriously make sure they know you love them. Methodically go through all the reasons why you appreciate them and are glad to be with them.
Then you can begin to make amends my repairing your damage. No, this doesn't mean going out and spending exorbitant amounts of money on champagne. You don't have to shower the house with rose petals for the next time they arrive home.
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What you should do is come up with a one-of-a-kind experience that involves a lot of effort on your end, and none on theirs. The experience will be a more powerful apology if it somehow references the beginning of your relationship, e.g. the place you first met.
Think you're home and hosed now? No, you're not.
A forgotten anniversary is a lasting commitment if you want to keep your relationship working. It might be a good idea to treat every weekend for the next month like an anniversary weekend (again, this isn't about spending money, it's about time).
It's a good gesture to cancel some future plans that your spouse knows you've been looking forward to as well. Just so it's clear you're putting them first. A concert or sports event you bought tickets to six months ago? That camping trip with your friends over summer? Scratch them, but don't preface this with, "If you want me to cancel this, I'll do it". Then you're just making your spouse the bad guy. You should throw another independent plan in the can proactively, and consider this a form of self-imposed punishment. Don't expect any congratulations for it, either.
Finally, tell your spouse they are to forget your anniversary next year. That's right, next time it's not their responsibility to remember the date, or do anything special. It will all be left up to you.
Start planning well in advance, get a countdown calendar app on your phone, and when the day itself comes you can pull out all the stops. A year on, then - and only then - may your forgotten anniversary booboo be wiped off your record. Lest you ever repeat it in the future, and then you're really in trouble.