I'm starting cancer treatment. How can I best take care of my mouth and teeth?

Detailed exam. If possible, you need to have a detailed examination performed by your dentist and have any problem areas addressed, especially if your cancer treatment involves the jaws and adjacent structures that are to undergo radiation treatment. Your dentist needs to work with your oncologist and vice versa to maintain your oral health and minimize any ill effects to your mouth from your therapy.
Mouth care. Talk with your oncologist about recommendations specific to the therapy you will be receiving. In general you will need to be careful with tooth brushing especially when your platelets / anc are low and you will want to use a mouth rinse at least after every meal. Mouth rinses are especially important if you are told not to brush your teeth.