I too inherited my parents' flatware, which we did use on special occasions. I knew very little about such things, but it was fun to research what other items were available in the pattern and pick up some stuff on eBay and elsewhere.
What I've read suggests that you can put it in the dishwasher, but it's probably better to hand wash. Be particularly careful with the knives, since the dishwasher heat can (over time) cause the hollow handles to separate from the blades. It's true that regular use keeps tarnish at bay; the tarnish is just rubbed off through the act of handling and washing before it builds up. You can also get these anti-tarnish strips to keep in the chest. They help with pieces that you don't use much.
phil wrote:I think you are supposed to arrange them in a certain order. forks on the left and something about smallest to largest or is it the reverse?
It's easy: the utensils go in the order they will be used. If salad is served first, then the salad fork goes on the outside; if the salad comes last, the dinner fork goes outside. If you're at a fancy dinner, just take the utensils from the outside in. Spoons or forks for desert go above the plate.