Stand on one leg, hold it for 15 seconds and switch legs. Try that drill everyday. Once it becomes easier, modifications to make it more challenging include holding it for longer lengths of time, stand on one leg with your lifted leg up behind you, try closing your eyes, that's a real challenge! You don't need special gear either. You can stand a squishy pillow, or hit the volleyball court at the local park.
Switch sides or hands with which you do everyday activities. Think of all the things you do with your dominate hand: brushing your teeth, opening doors, cabinets, stirring pots, mousing, eating, holding your phone, walking your dog, which shoulder your bag hangs on. . .now try the other hand or side. Check your feet too. Do you shift to one leg while standing? Try to shift to the other leg and try standing evenly on both.
Suck it up and in. If your abdominal muscles are weak nix that in the bud pronto. Also make sure your butt muscles are engaged too. By drawing in your abs and engaging the gluteal muscles your stabilize your pelvis which is foundational to good balance. Pilates is my favorite for improving your foundation.
Look up. If you have fallen and you fear that it'll happen again, so you stare at the ground you're actually setting yourself up for another fall. Keep your vision focused out in front of you. That 10-15 pound head of yours is just throwing off your balance if you always stare at the ground like you've lost the winning lottery.
Have a ball! Big ones, small ones, tennis, basket, fitness balls all can help with coordination which can help with balance. Try tossing a basketball between you and a partner. Start with just easy toss back and forth. Speed it up a bit. Try tossing the ball slightly off center to improve reaction times with your partner. Try tossing a tennis ball from hand to hand, tossing higher and higher. Another fun one is toss a tennis ball against a brick wall. Where that uneven wall will return the ball is anyone's guess!
Go outside and play. When was the last time you swung on a swing? Went up and down on the see-saw? Climbed on a jungle gym? It was called playing when we were kids. Now it's exercise. Your inner ear is challenged by the swing set. Control is required on the see-saw. And your coordination is required to scaling that jungle gym. And get out there soon. Playgrounds as we know them are changing. No more swings and slides. Now playgrounds are made up of blocks. Not sure what I think of this idea yet.
Well that's enough of this for now. And if you really have poor balance or these exercises make you nervous just reading about them, then talk to a competent fitness trainer first. You might want to work on postural exercises first. I talked about dysfunctional vs functional exercise a while back, so take a look.