Although some of these tips apply to any draft, there are some quirks that apply specifically to cube draft.
1. Draft a cohesive deck. In an environment where archetypes work, decks without a strategy are at disadvantage. That would not the case if the individual power of their cards were much higher, but since cubes tend to have powerful cards anyhow, the difference will rarely be worth the lack of synergy.
2. Two color decks work. That does not mean that monocolored decks don't, or that three-colored decks will be mana screwed too often, but there is no discussion that two colors is a good balance between effect variety and mana requirements. If you play only one color, the mana base will work very well, but the cards it powers might not be the best. Decks with three of more colors will have a harder time getting the right colors of mana, but will have access to a vast pool of cards. It should also be pointed that multicolored cards tend to be powerful, and monocolored decks don't have access to them.
3. Pay attention to the mana curve. It it easy to get carried away and draft 15 3-mana cards, but that means you'll either have to dump most of them to the sideboard or not get the most of your mana every turn.
4. Have answers or ways to play around most threats. A common mistake is not including artifact/enchantment removal. Some decks don't require that type of card, either because they win too quickly or can counter/discard them, but most of them are happy to play one or two cards in this category, as cubes typically include problematic artifacts and enchantments. This is true for creatures as well - creature removal is an important part of pretty much any deck.
5. Avoid antissynergy. In the same way that some card combinations potentialize each other's effects (combos), some combinations don't go well together. Pyroclasm, in a creature-heavy deck for example, will usually hurt you as bad as your opponent. Gigapede's untargetability, in a deck with several equipment and auras, is a drawback rather than a desired ability. Wonder and Levitation effects aren't very useful in decks with lots of fliers.
6. Don't load up on a card category. Too much removal for one type of card (typically creatures) will leave you with dead removal in your hand. Too much discard won't matter after your opponent is topdecking. Too much acceleration in a ramping deck and you'll have little to do with your huge amount of mana. Balance your deck, have varied effects, in reasonable proportions.
7. Stick to 40-45 cards. Smaller decks maximize the odds to draw the cards you planned your deck around. This helps cohesion and the proportion of land drawn will be slightly better.
8. Draft non-basic lands. You'll only play about 23 non-land cards out of your 45, so drafting non-basic lands - which don't take spell slots - may help your mana base and long term game.
9. Change your draft plan if you need to. Sometimes blue/white control simply isn't coming, so you might want to dump that plan and switch to blue/white aggro-control or white/red control using some of the cards you already got. Remember you'll only use about 60% of the cards you draft in your deck, so 40% can be left out. That being said, only switch plans if it's early enough - switching in the last pack is usually a bad idea.
10. Send signals and interpret them. A signal tells the players in front of you what you are playing, and that if they try to compete, they'll lose because they are in front of you. One valid strategy is to first-pick the color that has only one good card in the opening booster, and try to follow that color from then on. This highly decreases the chances that your neighbors will be competing with you. It is also important to watch the signals you're receiving. A very strong signal (not so much in cube because of card power) is a powerful card getting late-picked. In cube draft, some last picks are unbelievable (I've seen Phyrexian Arena and Scute Mob get last-picked).
There will be more tips in a post about archetypes in the near future.