You don't need special clothes to start with, but you will need trousers rather than shorts, and a long-sleeved top. Unless the weather is cold, thin clothes are advised so you don't get too hot. In poor weather or exposed areas a cagoule might be insisted upon. Trainers initially OK for shoes, but don't wear anything too nice as they will probably suffer from undergrowth in the forest, as well as getting wet and muddy - this applies to clothes as well. Once you become a regular, you will probably want to buy some special orienteering kit, and some hard-wearing, grippy, O-shoes.
The only fairly expensive equipment you need is a compass, but you might be able to borrow one if you don't have one. GPS is not allowed. A whistle is advisable, or even compulsory, in steep or exposed areas to call for help if you injure yourself and require help from another runner. Safety pins can be useful. If you come to larger events you'll soon get used to seeing the Ultrasport and Compass Point vans. Both sell a large range of orienteering kit and equipment. Both also run a mail order service.
It is advisable to take a change of clothes and shoes. You may want to take a picnic and a drink for after your run. Sometimes there is squash or water available at the finish, but some clubs prefer you to bring your own supply.
Toilet provision can vary from site-toilets to chemical-in-tent according to the formality of the event. Changing in usually done in your vehicle.
Make sure you have enough cash with you to cover any parking and entry fees.