There are a few types of resources within this game that you are going to have peasants working on gaining more of. They come in different forms, and when combined are used to create your force in Warcraft!
All species, even the undead, need food and such to grow. For this to occur, each of the seperate races must build a certain building to gain more food. For the humans, this is the house; for the Orcs, it's the burrow; for the undead, this is the Ziggurat, and for the Night Elves, this is the moon well. Some of these species have buildings which have special abilities as well, which will be covered in the profiles for those buildings. The maximum amount of food you can have is capped at 90, so for those who need to have tons and tons of troops, you might want to focus on the smaller units. Also, upkeep will occur at the points of 30 and 70, so keep an eye out for that!
When beginning a new game where you have control over your food and troop supply, consider building a large number of these food producing structures in excess early on, so that it's something you do not have to worry about as your army grows.
Finally, remember that each unit takes variable amounts of food to be built! For example, your typical swordsman will take two food to create, but the stronger and sturdier Knight will take three food. Some units, such as the Undead Frost Wyrm, will take a total of seven food! When making larger units, remember that you are doing so at the expense of possibly other units.
Gold is, arguably, the most important resource that you are going to come across in this game. While often you start off with one nearby, gold eventually runs out, so there is a "time limit" on all games in Warcraft because of it. However, usually it takes several hours for all the mines on a field to be overrun, so don't worry too much about rushing around and doing things. When it comes down to it, it's also the resource you are most likely to run out of. To gather gold, you have to be near it for most of the species. Humans need to build a Town Center near one, as do the Orcs. However, the Undead only need to summon it, a Necropolis does not need to be near by. The Night Elves need to be near as well with their main building, the Tree of Life, but they also have to wait for the tree to grow into the vine. For the latter two species, the minions do not have to run back and forth with gold, but can stay there. It's automatically added to the stockpiles. As seen above, this gives the undead the best advantage. It's also important, for this very reason, that you choose to expand. You can manage to win the game without doing so, but it will be very, very difficult in some cases if you try and take down all the enemies with roughly 13,000 gold available.
When you begin to build a large army, you will notice that it will take a chunk out of your upkeep at predetermined points in your army's growth. Be sure to use your army when you get the chance -- when you are at full upkeep, with only 3 out of 10 gold actually going into your coffers, you are loosing a massive amount of money each time you just let units hang around. If you have an army sizable enough that you feel comfortable charging out into the plains of battle, do so!
Wood, obviously, can be gathered from any of the standing trees on the map. While wood sometimes takes longer to collect, as many peons/peasants/etc as are required can be sent out to gather more wood as they need it. Also, in the expansion, a gnomish machine called a shredder is available, which allows you to down trees and to gather it at a fast rate, bringing back loads of 200 wood at a time. Two or three shredders can quickly bring a forest down to nothing. Wood is used more in buildings, while gold is more used in units. The more you have, the more buildings you can build at a faster rate. A reminder, however! When it comes down to it, forests are near impassable and most units can't damage trees, so if you have it to defend your base, don't let the peons discover and cut it, since it's only to your detriment!
Some units, however, such as catapults, will make short work of trees, so even if you have your back covered by a wall of trees, don't expect anything short of a forest to deter someone from making their own back way in!
Experience is the final resource which the game offers. Experience is a hero-centric resource which allows for heroes to advance levels, grow stronger, and get new abilities. It can be found through defeating enemy heroes, through defeating Creeps, and by using a Tome of Knowledge.