Upon colliding with a monster on the field, you will enter combat. The battle system in Dragon Quest VII is a fairly traditional turn-based affair, akin to older titles in the series, with not much changed from the original. At the beginning of each turn, you will choose all of the actions for your characters, then the turn will play out according to the enemies/team's speed. There are a number of options in-battle that you can pick for your characters, though.
Fight lets you choose a variety of options in which to attack, use items, defend or even flee. Attack lets you hit the enemy with your physical weapon, Spells are magic that you can use to smite foes or heal/buff your own characters, and Abilities are similar to Spells but aren't really considered magic. Items lets you pick an item to use in battle. Defend and Flee are just as they sound, the first mitigates any damage you take and the latter will make your party attempt to flee (it can fail).
Tactics allows you to change how the non-Hero characters behave in battle. Follow Orders mean you have complete control over their every action, while the other options will let the AI control them. Sometimes, it might be a good idea to have the other characters do what they want, as they can find weaknesses. You can also choose to Flee from the first menu (with Fight and Tactics), and Settings just lets you choose among various options that can be access from the normal Settings menu.
Note: Some pieces of equipment can actually be used in battle as items. For example, the Staff of Salvation can be used to heal a single ally.