Anyone can construct a Magic deck, but it takes strategy to win. A good deck has a good strategy to beat the opponent. Firstly, a primer on different tournament format, some cards may be banned or illegal in certain formats.
Wizards of the Coast releases new sets every quarter so there are different formats in which you can build your deck in. Generally, a new block is released every year and a Core Set every two years. Be sure to check the Banned/Restricted list to know which cards you can play.
Edit: I made an article showing a deck I constructed here.
Constructed (Player makes the deck):
Type II (Standard): Is the most popular tournament format. The deck must consist of cards from the most recent two blocks and the most recent Core Set.
Type 1.x (Extended): The deck must consist of cards from the most recent eight blocks and the three most recent Core Sets.
Type 1.5 (Legacy): The deck can consist of cards from any Magic set except the ones on the banned list.
Type 1 (Vintage): The deck can consist of cards from any Magic set except the ones on the restricted list.
Two-headed: Magic for four players. Each team consists of two players who share 40 life each. Everything else is the same, but rules for turns/attacking may vary.
Casual: Basically you can play any magic card you want and the rules vary according to the group of people you are playing with.
Limited (Draft/Sealed): A format where each player gets three/six booster packs, opens them one at a time, picks a card and passes it to the next player. The process goes on until all the cards from the first pack runs out. Then the process repeats until every pack is gone. Then each player adds his/her lands and makes a deck with the cards they picked.
The advice I can give about building a deck is based on Constructed mostly because Limited you have no control over who picks what cards.
There are three main types of decks: Aggro, Control and Combo. Many decks boast a combination of these types. When you are playing a specific type of deck, it’s called an archetype. The variety of different archetypes in your playing environment is your metagame. You want to build the type of deck that fares best in your metagame. A general rule to follow is that, Aggro beats Control, Control beats Combo and Combo beats Aggro.
Aggro decks focus mainly on one strategy: Attack. They have lots of creatures and lots of direct damage. I recommend this type of deck for beginners because it’s simple to play: just reduce your opponent’s life to 20. Green and Red cards are especially suited for this type of deck.
Some examples of the Aggro archetype below:
Green – Troll Ascetic, Tarmogoyf, Chameleon Colossus, Garruk Wildspeaker
Red – Goblin Piledriver, Mogg Fanatic, Lightning Bolt, Browbeat, Goblin Guide
White – Savannah Lions, Silver Knight, Baneslayer Angel
Blue – Clone, Morphling
Black – Nantuko Shade, Phyrexian Negator, Dark Confidant
Multi – Spiritmonger, Broodmate Dragon, Sarkhan Vol
Colorless – Aether Vial, Umezawa’s Jitte
Control decks focus on disrupting the opponent and maintaining control. These decks usually take longer to win than other decks. They often include counterspells, discarding, creature kill and defensive cards. Black, White and Blue are especially suited for this type of deck. Some examples of the Control archetype below:
Green – Harmonize, Ohran Viper, Eternal Witness, Kitchen Finks
Red – Earthquake, Wildfire
White – Path to Exile, Wrath of God, Worship, Windborn Muse
Blue – Cryptic Command, Fact or Fiction, Brainstorm, Daze, Redirect
Black – Thoughtseize, Duress, Diabolic Edict, Consume Spirit, Doom Blade
Multi – Blightning, Terminate, Lightning Helix
Colorless – Oblivion Stone, Mind’s Eye, Mindslaver, Batterskull
Combo decks focus on getting a certain combination of cards to win the game, often very quickly. These decks often require specific cards that have a certain role in the deck, many tutors, card drawing and mana accelerating cards are used. There isn’t one color specifically suited for Combo, as it depends on the cards used. Some examples of Combo archetype below:
Green – Doubling Season, Aluren, Earthcraft
Red – Seething Song, Rite of Flame, Dragonstorm
Blue – Mind’s Desire, Mind over Matter, Stroke of Genius, Mystical Tutor, Intruder Alarm
White – Replenish, Enlightened Tutor, Academy Rector, Orim’s Chant
Black – Vampiric Tutor, Dark Ritual, Yawgmoth’s Will, Necropotence, Tendrils of Agony
Colorless – Lotus Petal, Grim Monolith, Helm of Awakening, Tolarian Academy, Metalworker
Here’s the Enduring Ideal combo deck in action (my demonstration of a turn 4 kill):
…and the Hulk Flash combo deck in action (a turn 1!!! kill):