Designing your own schematics and PCB's (printed circuit boards) is fun and a lot less complicated than you think once you get started. There are a bunch of programs to design your schematics. KiCAD is a good one that is available for Windows, Mac and Linux.

A number of KiCAD tutorials that can be found online:

List of KiCAD tutorials

Getting started with KiCAD

KiCAD step-by-step

KiCAD documentation

Some other sources for help:

Dolf

The irc channel #electronics on freenode

All About Circuits

A few quick things to know when you get started:

Make sure you consult datasheets. Initially they seem intimidating, but when you read them you'll figure out they actually are very useful. The datasheet for the atmega328P (the same chip as an arduino has) on page 31 shows you how to wire a Crystal and accompanying capacitors to the chip.

You start with making the schematic containing all components and their connections

To prevent a mess of wires crossing each other in your schematic, use busses (blue thick lines)

Add values to your components, for instance the resistance or capacitance of resp. resistors and capacitors. A 10kOhm resistor would have the value 10k and a 10microfahrad capacitor would have the value 10u.

Add footprints for each component. Before making your layout, you need to tell KiCAD the size and shape of each component. You do that by assigning a footprint. It doesn't really matter which footprint you assign as long as it fits and the connectors (pins/legs) are in the right places. So whether you get the capacitor footprint exactly right doesn't really matter, as long as the spacing of the legs is the same and the overall space it takes on the PCB is the same too. Use google to search for which footprint you need for a certain component if you can't find it.

After completing the schematic with all their components and footprints, generate the netlist.

THen you start with laying the PCB out. You create a new PCB from the project view and read the netlist you just created.

Select a general layer setup. I usually work with a 2-layer setup with only parts on the front.

Drag all components to a “good” location. What good is is a matter of opinion, experience and some rules. We might want to add some rules down below for future reference.

Make a rule for yourself which connections/wires you put on the front and which on the back. I often choose for a perfboard design to put all horizontal wires on the front layer and the vertical ones on the back. That way you make sure they never cross each other. KiCAD won't let you put wires that cross each other on the same layer if they shouldn't be connected.

Often the PCB design is a process where you keep moving parts around, making the connections, deleting them again, moving stuff again, and redoing it until you're happy. There is no single right or wrong way of doing things. A lot depends on what the schematic is you're designing.

Some design rules:

always put a de-coupling capacitor between VCC and GND for a chip like the Atmega328P. A small ceramic disc capacitor needs to be put as close to the VCC and GND pins of the microprocessor like the Atmega328P. It is also often good to add a electrolytic capacitor (like 10uF) where the power comes into your board.

A microchip will usually need a Crystal oscillator as a clock to determine it's speed. The arduino (the atmega328P) uses a 16MHz Crystal. Those crystals also need 2 capacitors connected to it. I usually use 18pF ceramic disc capacitors.

Group your components according to function. All components that are working together should also be located close together. So for instance the Crystal and it's two capacitors should be located very close to each other and preferably right next to the pins of the atmega328P that they need to connect to.

If you order a printed board online eventually, look at creating a ground plane instead of connecting all GND pins with wires.

See also http://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter12.pdf