For those using the pre-release 1.0 version of CocoaPods, the 'link_with' directive that @samuel used is deprecated. I tried simply adding my playground as a target in my Podfile, but CocoaPods doesn't recognize it as a valid target.
I found that adding a scheme for the pod I need to use and building it manually works as discussed here.

To demonstrate this in action, I have created a sample project with Alamofire integrated into a Playground here.
I also came across this library. I haven't had a chance to use it yet, but it looks promising.
Aside: if you'd like to make asynchronous requests in a Playground (e.g. with Alamofire), you'll need to enable indefinite execution as described here.
I hope this helps.