Ash, there are a lot of leagues around the Livonia area. Some only accept team registrations, but some accept individuals as well.
Here are the leagues I know of that accept individuals. Either they are draft leagues, will place you with teams looking for players, or have sub lists:
www.rspi.net/ Plymouth/Canton area rinks
www.suburbanicefarmingtonhills.com Suburban Ice in Farmington Hills (beginner league)
www.hna.com Hockey North America (Dearborn, Melvindale, City Sports in Detroit)
There are other leagues that only take full teams:
Livonia, Garden City, Hat Trick Hockey (Canfield/Redford), Farmington Hills...
And plenty of other leagues if you're willing to drive, like Troy, Royal Oak, Hazel Park, Detroit Skating Club in Bloomfield Hills, Kensington Valley in Brighton, MSE in Trenton, Fraser, and Mt. Clemens, Rochester Onyx, Ann Arbor Ice Cube...
Your best bets are to talk to any friends who play in a league and see if they need subs or know of any teams looking for players, and to hit up some of the local rinks for drop-in hockey or "sticks and pucks" and talk to players there.
I play in the Livonia league on Friday nights, it's pretty well-run and competitively balanced, we have a lot of fun!
Good luck, I hope this helps!!