Production is important
Sometimes Hero control, spell casting, and luck can determine a winner. However, quite often the more resources you harvest and mine and the higher level units you produce or the upgrades you research will determine who wins the game. You need to secure additional Gold Mines and make sure you harvest enough Lumber.

Get your Economy Going
It is important at the beginning of a game to get your economy rolling. This means training workers to harvest Lumber and build buildings. Continually train workers in a steady succession from the beginning. Once you have enough workers, stop training. You will find that you may need additional workers if you need to build several buildings at once, you start building units or researching upgrades that require a lot of Lumber or when you expand to another Gold Mine.

Keep your Economy Going
Build Expansion Towns. Watch your Gold Mine and make sure you get additional Gold Mines before it runs out. Try not to be placed in a situation where you have to look for another Gold Mine and are not currently mining Gold.

Workers on Gold
Night Elves and Undead only need 5 workers on each Gold Mine. Any more units placed on the Gold Mine will be wasted. Orcs and Humans may need more than 5 workers when the Town Hall (or Great Hall) is placed too far away from the Gold Mine.

Lumber
Be careful not to harvest too much Lumber. If you are limited on food and find yourself with too much Lumber, kill off some harvesting workers to free up food. Some units require Lumber to produce. If you build a lot of these units you may find you need to place additional workers on harvesting Lumber.

Whenever possible purchase a Goblin Shredder. One Goblin Shredder can replace all of your workers that are harvesting Lumber. You can then kill them off to free up food or use them to clear away the trees blocking Gold mines for making expansions

Keep Your Resources Spent
Do not save up Gold and Lumber. Warcraft III is not won by accumulating wealth, but rather instead by crushing your enemy. If you find you have too much Gold and Lumber, spend it on more units, unit producing buildings, and upgrades. In team games, ask other players if they need any resources and distribute them to your team. You cannot always keep your money spent but keeping money spent is a good overall plan. It is often very embarrassing to lose a game when you have plenty of resources but just did not bother to use them properly.

Resource Upgrades (Humans)
Get the Lumber resource Upgrades so that you can Harvest Lumber faster.

Borrow and Share
Use the resource trading options in Multiplayer game to give resources to your allies when they need them and to ask for resources when you need it yourself.

Upkeep
Pay attention to Upkeep and how it affects your economy. You may need to reduce the number of units to drop a level in Upkeep to generate additional resources. Another option is to take over more Gold Mines to balance the higher Upkeep.

Out of Gold?
If you find yourself in a situation where your Gold Mine has ran out, you're out of Gold, and you don't have an additional expansion there are some options:

All Races
Use your army to kill some Creeps. The Creeps will generate Gold which you can use to build a new Town Hall.

Players of all races can - if they dearly need gold ASAP (e.g. for haunting a mine) - have their Heroes sell some/all of their items to shops (owned/allied/neutral). Though this can make the Heroes at least temporarily weaker, it often proves worthy, because it's better to have a new gold mine being harvested, than to have a strong Hero without an army to lead. If you sell items that are available in shops, you can buy them back once you have the gold stream reestablished again. This is most useful in longer solo games and perhaps some FFA.

Orcs and Humans
You will need to "long distance mine". Instruct your Peons and Peasants to travel to the next closest Gold Mine. Gather some Gold and walk it all the way back to your Town Hall. Continue this until you have enough to build a Town Hall at a new Gold Mine.

[ Click to Enlarge - 183 KB ] This player must walk Gold back to his Great Hall long distance because he is out of Gold and his Gold Mine has collapsed.

Orcs
If you have researched the Pillage ability you can attack enemy buildings for resources.

Night Elves
Uproot your Tree of Life and walk it to the next closest mine. You may wish to research Nature's Blessing before walking there so that the Tree of Life can get there much faster. You should do this with every Tree of Life once they have mined out a Gold Mine.

Undead
Undead players should unsummon some of their less important buildings to get enough Gold to create a new Haunted Gold Mine.