How do I obtain medkits?

You can purchase them from traders who fly over. When you get a notification that a trader is passing by, direct one of your colonists to a comms console and call the trader. From there, it will list what they have for sale and what you can sell to them. You'll need a orbital trade becaon so that the trader has somewhere to drop the goods.

You can read more about Trading on the Rimworld wiki: http://rimworldwiki.com/wiki/Trade

In the base (un-modded) game, Medkits are obtained via trade. You may wish to try the mod Simple Medicine Craft, that lets you create Medkits from cloth and berries.

Now as of Alpha 8, a new Herbal Medicine item can be created from Healroot (a growable plant).

Herbal medicine has a cap of 70% effectiveness, while standard medkits have a cap of 100%.

As of 1.0: https://rimworldwiki.com/wiki/Medicine

Medicine can either be purchased from traders, looted from raiders, or crafted at a drug lab using 3 cloth , herbal medicine and neutroamine (skill requirement: medicine 6+ and crafting 3+, the pawn must also be capable of intellectual work).