There are several strategies.
Change the whole focus of the sentence. For instance, you want to flatter the person by asking "did you cook this meal yourself?" (knowing that he/she did cook it indeed), you'd be tempted to ask avez-vous cuisiné ce plat vous-même? ; you'll have to ask ce plat est délicieux, qui l'a cuisiné ? instead.
For "your", instead of ton/votre, always use ce. You want to borrow something, you won't ask it like "puis-je emprunter ton/votre ..." but either "puis-je emprunter ce ...".
If talking to someone you know very well from an organisation, like a different company, but you're not sure of the context (formal/informal?) just always say vous and pretend you talk about the organisation as a whole, which is always a plural, if you get any remark.
Sometimes, you just can't. In this case, use vous repeatedly until the person makes clear that the tu is ok. :)
Some people have the dirty habit of using neither vous nor tu but will use a third-person instead. Typical from shop owners who want to sound a little fancy: Et il lui faudra quoi au monsieur? Do not do that.
Another trick as I discovered by answering another question : sometimes, you can use nous:
- Ne nous énervons pas!
- Comment allons-nous ce matin?
- Prendons-nous du sucre avec notre café?
I'm not saying it's always applicable, and it will sound weird in a lot of cases, but it's worth knowing.
As already mentionned, the third person can also be used, but probably only butlers can pull that one off:
- Monsieur a-t-il bien dormi?
- Madame est servie.