Add a `tsconfig.json` and turn on `allowJs` for starters. If you're already using Babel, you can check out the Babel/TypeScript Starter for some guidance on quick and easy integration [1].

Then create a `types.ts` file for types that are used throughout your project, and as you see common data structures being used in your program, declare `interface`s and `type` aliases there. Then you can switch your `.js` files to `.ts`/`.tsx` files one-by-one and add types (or even add types via JSDoc and then convert those to `.ts` files when you're ready).

Eventually for the best experience, you can start switching on strictness modes. `strictNullChecks` is a pretty great one to use early on. Then `noImplicitAny` and `noImplicitThis` when you have pretty good type coverage. Finally you can turn on the full `strict` flag which will turn the others on, which are pretty easy to integrate into your codebase (and which you can turn off individually).

[1]: https://github.com/Microsoft/TypeScript-Babel-Starter