I have used many schematic/PCB capture applications and I find that Cadsoft Eagle seems to be the standard for hobbyists. As such, there are some peculiar features that takes some getting use to. For instance, the user interface does not function like many point-n-click applications. You can Google eagle tutorials and find plenty.
Below are some of my favorites:
This tutorial demonstrates how to measure voltage across a potentiometer. The concepts explained in this tutorial can be used to create position feedback sensors and contrast/brightness control for Liquid Crystal Displays. Check out the tutorial for full details.
This tutorial demonstrates using a Light Dependent Resistor (LDR) to vary the blink rate of a LED based on the level of light striking the LDR. This tutorial covers some basic concepts that can be used to develop home automation applications such as automatic light dimmers, automatic blinds or curtains and a automatic night-light. Check out the tutorial for full details.
This tutorial demonstrates uploading sketches to an Arduino over a wireless connection. I designed a couple of XBee adapter boards for my Hobbyduino V3 (Arduino clone). These adapters made it easy to properly configure each of the XBee Series 1 modems used in the tutorial. Check out the tutorial for full details.
Hobbybotics 