To multiclass, you spend a level-up taking a level in a new class instead of your current one. Your total character level is the sum of all your class levels, and it’s what sets your proficiency bonus — so multiclassing never changes how well you hit or save.
There’s a gate: you must meet the ability score prerequisite — usually a 13 — in the key ability of both the class you’re leaving and the one you’re joining (see the table). A Fighter dipping into Wizard, for example, needs Strength or Dexterity 13 and Intelligence 13.
The trade-offs are real: class features and Ability Score Improvements come slower, you may miss a class’s high-level "capstone," and spellcasting gets fiddly (spell slots combine on a special table, but Warlock Pact Magic stays separate). Multiclass for a concept or a specific combo, not by accident.