We recommend using one of the official SDKs, such as the official Dropbox SDK, whenever possible, as it will do much of the work for you.
If you can't or don't want to though, for whatever reason, you can certainly use the HTTPS endpoints directly. I see you've already found the documentation for those, but there are also a number of guides that may be helpful. You can also use the API v2 Explorer to test out calls.