Playing 'outside' is a great way to add the element of danger to a guitar solo. It is usually understood as meaning outside of the key center. However, the knack is to make it sound convincing as opposed to making it seem like you are just playing a bunch of wrong notes. The trick to making it really work is essentially; strong articulated phrasing, knowledge of the harmony you decide to use and stepwise resolution. If you are new to this I would advise you to keep your outside phrases short and to the point. Long phrases require more conviction and a little more experience. Harmonically, you can experiment with just about any un-related key but you might want to start with the obvious at first, to really get the hang of it. ie; up or down a half step. The most important thing to work on is getting back to your home key in the strongest, most effective way. Here you might focus on 1) targeting home key chord tones, 2) resolving home by step (that is, falling naturally on to strong, essential chord tones) and 3) stressing your home key by outlining a triad. In the following examples I have used a D minor key throughout.

Example (b) shows how using a dominant phrase (in this case A7b9) effectively gets you back to your home key.

Example (c) shows the "in-out-in-out" melodic idea where you alternate an "in" phrase with an "out" phrase. In this case I have chosen a tritone to play with but you could experiment with just about anything. Again, the home key, when I finally get there, is well and truly stressed. Have fun!