Though others will probably disagree, I think synthetic oil is overkill in these engines, and there is some risk that new oil leaks will develop if you switch with a lot of miles on the seals etc.

I live in northern Virginia, where it gets moderately cold in the winter (10F is not unusual, occasionally down to 0) and hot in the summer (highs in the low 90s, sometimes for weeks at a time, over 100 once or twice a year) I use, per the recommendations in the owners manual, 10W30 in the winter, and 15W40 for the rest of the year. For the 15W40, I like Shell Rotella, and the 10W30 can be any reputable brand, such as Castrol, Valvoline or Pennzoil. (avoid cheap generic oil) If your engine uses little or no oil, you can probably use 10W30 year round, unless it gets really hot where you live, or below zero for any length of time.

If you don't have an owners manual, the temperature ranges are:

5W30........up to 68F
10W30......-4F to 104F
15W40......10F and up

You change the oil and the filter at the same time. You will need a wrench for the drain plug, an oil filter wrench, and a pan to catch the oil in. With the engine warm, remove the plug, and let it drain for a while---10 minutes is a good minimum, but within reason, the longer the better. Using the filter wrench (the kind with a smooth metal band that goes all the way around the filter and a handle that swivels from side to side works well for me) unscrew the oil filter. It is full of oil, and will be hot. The engine block and particularly the exhaust manifold are also hot---you may want to wear work gloves. Once it is broken loose with the wrench, the filter should unscrew easily by hand. Some oil will spill when you remove the filter. try to avoid getting it on the motor mount. I saw recently where someone suggested covering it with aluminum foil to protect it. Keep the open end of the filter pointed up, until you can empty it into the drain pan. Make sure the old rubber gasket is not stuck to the side of the engine. Apply a small amount of oil to the gasket on the new filter and screw it on. If you have a strong grip, you can tighten the filter sufficiently by hand, if not, use the wrench again, but don't get it too tight. See the directions on the box or the side of the filter. Put the drain plug back in and tighten it (again, not too tight) It is a good idea to replace the copper washer that goes between the plug and the oil pan. You can usually reuse them once or twice, but beyond that, they will no longer seal well, and you will have an annoying drip. Fill the engine with oil. Put the old oil in a suitable container for recycling. Let the old filter drain thoroughly, and find out waht you are supposed to do with it---some areas don't want them in with the regular trash, others don't care.