Keep a unit/building selected.
1. The key "B" is your biggest ally. B when a worker unit is selected takes up the "Build" screen, this is the reason the top players are able to begin building production right out of the town hall.
2. A second quick way to learn a skill for a hero is "F1 + O + (skill hotkey)"
3. Ctrl + (1-0) is another game winner. These keys make it so much easier to micro it isn't funny.. usually you'll use the keystroke 1 as melee, and this combination: 1 + A + click (not on a unit) to command them to pretty much be on alert, focus firing with melee isn't very good. A second would be setting your ranged group to "2." When group 1 is set and fighting, focus fire with the ranged, after being sure you hit "2" to take out their ranged.
4. Ctrl also works on groups of similar buildings, like 2 Arcane Sanctums. When viewing a battle, it's extremely easy to hit, say "8-S" to begin production of Sorceresses, or "8-P" for Priests.
5. Search for your heroes ability hotkeys. The quickest way to get a Water Elemental off with an Archmage is to just quick hit "F1 - W" instead of clicking on the Archmage, then finding the WElemental icon, and clicking.
6. Some hotkeys are obnoxious to learn, and you can find customization sets all around the WC3-based sites, such as Warcraftstrategy.com.