General:
* Fiddling
* Muddling
* Dabbling
* Pottering
* Fooling around
* Playing around
* Experimenting
* Working on
* Fixing
More specific:
* Repairing (if you're fixing something)
* Modifying (if you're changing something)
* Improving (if you're making something better)
* Creating (if you're making something new)
* Building (if you're constructing something)
More informal:
* messing about
* monkeying around
To get a more precise word, tell me:
* What is being tinkered with? (A machine, a piece of furniture, a recipe, etc.)
* What is the goal of the tinkering? (To fix something, to improve it, to make something new, etc.)
For example, if you're "tinkering" with a car engine to make it more powerful, you might say you're "modifying" or "improving" it. If you're "tinkering" with a recipe to make it tastier, you might say you're "experimenting" or "playing around" with it.