Natural light shapes a photo; artificial light lets you design one.
Light modifiers change quality without changing the source: softboxes and umbrellas enlarge a source relative to the subject, softening shadows; reflectors bounce existing light back to fill shadows; diffusers scatter hard light into something softer.
Off-camera flash — moving flash off your camera's hot shoe, triggered wirelessly — is the single biggest step toward controlled lighting, since it lets you position light relative to your subject rather than always firing from your shooting position.
One-light, two-light, three-light setups: one light (often paired with a reflector) teaches you how a single source shapes a face — the foundation everything else builds on. Two lights typically add fill or background separation. Three lights (key, fill, hair/rim) give full independent control. Add complexity only when it solves a specific problem — many strong portraits use a single light.
Mixing ambient and flash: set ambient exposure first via shutter speed and ISO, then add flash power to light your subject — shutter speed controls how much ambient light you gather, flash power controls your subject, largely independently of each other.