A Magic Turn

Turns in Magic are critical to understand.  The Intro page gives a quick overview; this post gives more detail.

But first, a fundamental concept. During your turn, you are the active player.  In each step of each phase, you go first.  But after you choose what to do, your opponent(s) may choose to play instants, cards with 'flash', or use abilities.  And if you choose to 'pass' on a given phase, opponents can still perform allowable actions. In the same way,

101.4. If multiple players would make choices and/or take actions at the same time, the active player (the player whose turn it is) makes any choices required, then the next player in turn order (usually the player seated to the active player’s left) makes any choices required, followed by the remaining nonactive players in turn order. Then the actions happen simultaneously. This rule is often referred to as the “Active Player, Nonactive Player (APNAP) order” rule.
Example: A card reads “Each player sacrifices a creature.” First, the active player chooses a creature they control. Then each of the nonactive players, in turn order, chooses a creature they control. Then all creatures chosen this way are sacrificed simultaneously. [from the official rules]

Understanding this "APNAP order" can be important in certain situations.  Now, on to turns.

Each turn has five phases. Each phase occurs even if nothing happens during it.

1) Beginning Phase

• Untap: 
• Untap any tapped cards you have on the battlefield.  
• No one can play spells or abilities during this step. 
• Upkeep: 
• Abilities that trigger at the beginning of your upkeep go on the stack. 
• Players can play instants and activated abilities. 
• Draw: 
• Draw 1 card from the top of your library (note: this step is skipped for the first turn of the first player). 
• Players can play instants and activated abilities. 

2) Main Phase

• Play up to one land (put it from your hand onto the battlefield).
• Cast spells if you can/want (by tapping lands to pay a spell's mana cost, putting it on the stack, and resolving its effect).
• Players can play instants and activated abilities.

3) Combat Phase

• Beginning of combat: 
• Any card effects that happen 'at the beginning of combat' happen now. 
• Players can play instants and activated abilities.
• Declare attackers:
• You choose which of your creatures will attack (if any).
• Tap creatures that are attacking. Creatures with 'defender', already tapped creatures, and creatures with summoning sickness cannot attack. 
• For each attacking creature, declare your target. You can target only your opponent(s) and/or their planeswalker(s). Once you're done declaring, players can play instants and activated abilities.
• Declare blockers:  
• Your opponent decides which of their creatures will block your attacking creatures (if any) and assigns one or more creature to block each attacker. 
• Only untapped creatures may block.
• Once your opponent is done declaring, players can play instants and activated abilities. 
• Combat damage:
• Unblocked attacking creatures deal damage equal to their power to the target (the defending player or planeswalker).
• Blocked attacking creatures deal damage equal to their power to the creatures blocking them.  If more than one creature blocks an attacker, you decide how to divide the attacker's damage among the blockers.
• If a creature has left the battlefield since it was declared a blocker, the attacking creature does NOT deal any damage to the defending player (even if all blockers have left the battlefield).
• The blocking creatures (the defenders) deal damage equal to their power to the creature they're blocking.  
• If a creature has become tapped since it was declared a blocker, it still deals damage normally.  
• If a creature receives damage greater than or equal to its toughness, it dies (goes to the graveyard).  
• If a creature receives less damage than its toughness, it remains on the battlefield with the damage still on it.  
• End of combat: 
• Any card effects that happen 'at the end of combat' happen now.
• Players can play instants and activated abilities.

4) Main Phase

• Play up to one land (if you haven't already done so).
• Cast spells if you can/want.
• Players can play instants and activated abilities.

5) End Phase

• End: 
• Any card effects that happen 'at the beginning of the end step' happen now. 
• Players can play instants and activated abilities.
• Cleanup: 
• If you have more than seven cards in your hand, choose and discard cards until you have only seven.  
• All creatures heal (the damage is removed from those still on the battlefield who have received less damage than their toughness)
• "Until end of turn" effects end.  
• Players CANNOT play instants and activated abilities. 
• Your turn is over.  Play passes clockwise; the player on your left now takes their turn and becomes the active player.

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The parts of the turn are nicely summarized on this image:

Originally from Wizards of the Coast; retrieved from this site

These turn & combat structure aids are helpful; re-posted as found on the 'Budget Magic' Facebook group:

One final comment: taking actions on other people's turns (through instants and activated abilities) can be an important strategic element to the game.  More on this later.