Can someone please help me figure out how to best travel around Thailand within 10 days? i would like to go to Bangkok, Ko samui, Phuket, Chaing Mai, and see some of the rural areas of northern Thailand. As for Ko Samui and Phuket, i cannot figure out how to fly between those two islands without first flying back to Bangkok which sems like a waste of time and money. Please advise.

I think you are trying to cover too much territory in 10 days. One needs to take it easy in SE Asia - things move at a slower pace and the heat/humidity will also wear on you if you try to do too much. You will get many comments here so let me start things off by suggesting you stick to 2 destinations- Bangkok - 4-5 days and then a beach resort for the remainder- maybe Phuket.

That is a great deal to do in such a short time, there is little point going to both Samui and Phuket as they are fairly similar, there are 1 to 2 flights per day from Samui to Phuket, not sure why you thought you would have to go via Bangkok(?).
If you only have 10 days I would spend a few days in bangkok ( if you are into busy cities) and then just a couple of hours by road takes you to the River Kwai area where you can find river, river rafts, jungle, elephant rides, soft adventure activities, find also temples etc, then head down to a beach for a week. Time of year can dictate which beach/island you head to but Samui or Phuket is you want busy islands plus entertainment etc.

You will find that most travellers on this board will suggest that is too much to cover within that time frame, and offer plenty of good reasons why. However, if you are stubborn like me, or just feel you want to see as much as you can, my recent post 'Thailand Itinery - Airfare Purchased - Please Add Suggestions' is similar to your agenda and if you click on my name you can see the threads that helped lead me to that decision.

Here's my two cents worth. Each time you change locations, you will "lose" approximately 1/2 day. The places you want to see suggest air transportation. Transfers, check-in, flight, and luggage retrieval. If you start and end in BKK with three other locations, that is about 2 days travel. With 10 days, that would be too much travel for me. However, if you are young and energetic and can get early flights, you can logistically accomplish it. But as JamesA notes, visiting both Phuket and Ko Samui would seem to be duplicative. Phuket is easier to get in and out of. If you skip Ko Samui, BKK-CM-Phuket-BKK is do-able.