Homemade methods for interfacing a Servo with LEGO bricks
The best solution is to create custom LEGO-compatible bricks that your servos (or other parts) fit into. This can be done by: 


modding existing bricks with knives, glue and other tools
building bricks from other material (wooden LEGO, formed with Fimo/Sculpey...)
building bricks with a 3D-printer (for instance see the LEGO category on thingiverse). There are online services to print your designs if you don't have a 3D printer (yet ;-)


Each strategy is worth another question here at bricks.SE.