I use 3 different ways...
1: For quick & easy prototyping, nothing beats a solderless breadboard.
2: For simple/quick & rugged/permanent construction, I use pad-per-hole vector board and point-to-point soldering. The boards I use are some I had custom made years ago, when one of the PCB fab companies had a great 100 piece price and didn't care if it had too many holes (most won't honor low prices for making these boards). You can see them on many pages where I've tested Arduino libraries. For example:
http://www.pjrc.com/teensy/td_libs_Keypad.html
Back then, everyone had high prices on pad-per-hole vector boards. Recently there are a number of companies like iTead which have them very cheap. Here's one:
http://imall.iteadstudio.com/prototyping/protoboard/im120710002.html
The downside to point-to-point wiring is it's time consuming. I use Teflon insulated wire, which helps a lot since the plastic doesn't melt or shrink if you heat the wire too much while soldering. It costs more than normal wire, but the time saving is worthwhile.
3: For complex & rugged/permanent construction, laying out a custom PCB is the simplest way. Well, that's after you suffer the learning curve of the CAD software. Unfortunately, you can't have both fast and cheap. For fast, I use
www.pcbexpress.com. For cheap, I usually use
www.oshpark.com, but if the board is much larger than about 10 square inches and doesn't need the higher quality specs, I'll use iTead. But Oshpark's quality is much better. Sometimes using 6 mil traces and 13 min vias saves a lot of time routing the board and allows a smaller size, which makes oshpark even more attractive.