How do we play?

First and foremost, an MTG cube is designed to be used for drafting. If you're not familiar with how to draft, I detail that below, along with some general tips to help get you started. The basics of drafting are easy, but there's a lot of depth to explore. I recommend starting simple, and letting experience be your guide. Reading up will only get you so far — you gotta play!

A normal Magic draft uses unopened booster packs of cards, and calls for 8 players. (Less than 8 players is fine, but a full 8 is ideal.) For a video demo of what the process looks like, the makers of Magic have a introductory guide to drafting here. Each player has 3 booster packs, and all the players sit in a circle around a table. When the draft begins, the steps are as follows:

1. All 8 players open pack #1 at the same time.
2. Pick a single card to keep for your deck, and pass the rest of the cards to the left, facedown.
3. Look at the cards that were just passed to you, pick another single card, and pass the rest left again. Continue looping this step until all the cards in the pack have been chosen.
4. Everyone opens pack #2 at the same time, as before. Repeat steps 2 & 3, but now pass leftover cards to the right each time.
5. When pack #2 is done, everyone opens pack #3 at the same time, and repeats steps 2 & 3. Pass leftover cards to the left again.

At the end of this process, each player will have drafted 45 cards to use in building a 40-card deck. In addition to the 45 drafted cards that are yours to use, each player also has access to an unlimited amount of basic land cards, usually sitting in a box nearby & ready for borrowing. A typical 40-card deck has 17 lands, and 23 spells (creatures, artifacts, sorceries; anything other than a land, basically).

The only change to the above steps when you're drafting a cube is that the cards don't come in a sealed booster pack. Instead, part of the setup for a cube draft is to recreate sealed packs: the card pool is shuffled and then made into "stacks" of 15 cards. Once there are 3 stacks per player ready to go, the pre-draft prep is done and drafting proceeds normally.

Drafting tips and strategy

That's the nuts & bolts of the drafting process covered. But how to approach it as a player? What can you do to help yourself win? The main skill to develop is called card evaluation: the ability to look at many cards and understand which options are better than others. One mnemonic that some players use to guide how they look at cards is the acronym BREAD. That stands for bombs, removal, evasion, aggro, and duds.

Bombs. These are splashy, powerful cards that sometimes are enough to win a game on their own. In the cube I've built, all the cards are common-rarity, so there's a much flatter power curve, and what stands out as a "bomb" is very different. Any creature with a power and/or toughness of 6 or higher is pretty much a bomb in this cube, for example, especially if the creature includes other effects or abilities too.
Removal. Cards that get rid of an opponent's stuff! It might destroy a creature outright, deal a set amount of damage, inflict -X/-X stats until end of turn, force a player to sacrifice something, and so on. Removal also includes preventing cards from being played: both discard effects and spells that "counter" cards while they're in the process of being cast.
Evasion. Creatures with keywords like flying, trample, menace, first strike and so on make it difficult for your opponent to block and/or prevent damage. Folks sometimes also include efficient cards under this letter: a creature might return health to you with lifelink when it deals damage, or otherwise present you with multiple options and flexibility. For non-creature spells, any card you play that also lets you draw a card, scry, or search your library for a card is generally "efficient". You get a new card in hand to replace the one you just played, or otherwise "thin" your deck — meaning, you've made it more likely your next draw will be something good you can use!
Aggro. These are all the creatures that aren't very fancy, but will put in the work to attack, block, deal damage, and so on. Most of the creatures you draft will probably fit this mold. A good aggro card has a nice ratio of cost to size, such as 3 mana for a 3/3 creature, or even something pushed a bit further like a 3/2 creature for 2 mana. The main keyword to look for here is haste, which lets you attack with a creature right after playing it. The first strike keyword (mentioned above under evasion) is aggro-friendly too, as is double strike.
Duds. Also known as dregs, these are the cards you should never pick first. Sometimes they're underpowered, or straight up bad cards. This the other end of the scale where the cube format matters: I've handpicked all the cards, and duds should be few & far between! More than any real "duds", there might be cards which are only situationally useful, or otherwise hard to play for good effect. Sometimes I also include defensive cards here: playing pure defense rarely wins games, but if you don't have anything else good to pick, something that helps keep you alive & in the game (like a high-toughness creature with defender) is still playable.

In a draft, you also bring in knowledge of the draft environment. What sorts of cards pop up a lot? What cards hardly appear at all? In this case, you can check out the full list of cards in the cube for an idea of the environment.

Layered on that is your knowledge of what you've picked so far. (You can look through your chosen cards at any time while you're still drafting.) You want to have a good mix of creatures and other spells. In many respects, creatures are the core of Magic decks, for reasons I won't delve into here. In a 40-card deck, with 17 lands, it's typical to run 15-17 creatures and 6-8 other types of spells.

There's also what your cards cost to cast! This side of deckbuilding is called the mana curve. The ideal is to be able to play cards every turn, and make the most of the mana you have available. And to do that, you need a spread of cards that are 1-mana, 2-mana, 3-mana & so on to cast. Cards with high mana costs make a big impact in games, but take more turns before they can be cast due to their expense. If all your cards are expensive to play, you'll might lose before you have a chance to use them.

As a beginner, all that can be tough to keep in mind to at once! And it's why experience is the best teacher, too: having too much research and concepts to juggle mid-draft can lead to serious analysis paralysis. The most important thing is to keep doing what's fun for you, even if it runs against what might be the min/maxed "most optimal" decision. If you're still having fun, you'll keep drafting, and you'll find yourself picking up a lot of wisdom about playing the game as a byproduct.