At any level, you can take the multiclassing feat for one other class. You can only ever multiclass to one other class. That feat makes you count as that class, as well as your own, for all feats and paragon paths. That feat also gives you limited access to some of that class' abilities on a limited basis.
Starting at 4th level, you can take the Novice Power feat, which allows you to switch out an encounter power. You give up one of the encounter powers you gained with your class, and gain an encounter power from your multiclass.
Starting at 8th level, you can take the Acolyte Power feat, which allows you to swap out a utility power as with the Novice Power feat.
Starting at 10th level, you can take the Adept Power feat, which allows you to swap out a daily power as with the Novice and Acolyte Power feats.
If, and only if, you have taken all four multiclass feats, you can then choose to take your multiclass as your paragon path. When a paragon path would normally give you a power or ability, you instead gain powers or abilities from your multiclass, meaning that you gain another encounter, daily, and utility spell from your multiclass. The encounter power must be of 7th level or lower, the utility of 10th level or lower, and the daily of 19th level or lower.
You always retain the HP level rate of your initial class, and the armor/weapon proficiencies of that class (as well as any feats you may have spent to gain new proficiencies).