Wash Your House
This job can be done without a power washer, but it will be much more labor intensive. Using a bucket with detergent and a large soft scrub brush attached to your extension pole, wash your house in sections and rinse off as you go. A general rule of thumb whether doing it by hand or with a power washer is to wash from the bottom up, and rinse from the top down.
The price of power or pressure washers has come down in recent years. If you want to buy your own, search this site for how to buy a power or pressure washer. However it is more economical for most homeowners to rent a large gas powered washer for a day or weekend. The rental yard staff will give you instructions on how to use it.
It's possible you may be able to get by with just a good powerwashing without detergent if all you have is surface dirt and cobwebs. Chances are you will need a more thorough cleaning. Most power washers have hose feeds which mix in the detergent so you can soak your house in small sections, then flip the switch and rinse it with a powerful spray. If you have any mildew, you must use chlorine bleach to kill it. Paint and hardware stores carry detergents that are formulated so that you mix in the bleach, then after it has been applied the bleach is neutralized before the chemicals can get up under your siding and do lasting damage. One brand to look for is Jomax.
Before you start, tightly close all windows and doors. Either keep the spray away from lights and electrical outlets, or cover them with plastic (duct tape will hold up to water.) Move lawn furniture, flowerpots and anything else out of the way. Cover landscaping close to the house with plastic sheeting, and weight it down, otherwise the water blasts will blow it away. Check the link below to learn how to find and get rid of wasp nests before starting. Water won't really deter them, it just annoys them.
Wear safe, nonskid shoes especially if you will be on a ladder. Sunglasses or safety goggles are a good idea too because you will be kicking up debris. Choose a warm day without any wind. In fact the hotter the better, it's a great way to stay cool!
Start powerwashing. If you are using detergent, you'll spray that on first at low pressure and give it a couple of minutes to work, before switching off the detergent valve and rinsing at full pressure. Doing areas about ten feet square at a time works well. Be careful with the wand at full pressure, it can do real damage if used improperly. You will probably use the general purpose nozzle (usually yellow) which will give a pretty powerful blast. Start standing well back and get a feel for it. Be especially careful with wood and other softer surfaces, as you can gouge it quite easily if you get too close. Also don't direct the spray directly at windows as you can break the glass, the seal, or both. Whenever possible, spray perpendicular or slightly downwards, if you are washing siding. You want to avoid forcing too much water up underneath the siding where it can damage the sheathing.