What Alternate Picking Actually Is
Alternate picking isn't some separate advanced technique - it's a simple rule: every note gets a picked stroke that alternates down-up-down-up, with no exceptions, even across string changes. It's the strictness of the alternation, not the speed, that separates alternate picking from playing 'however feels convenient'.
A rule with no exceptions
Everyone feels the temptation to sneak in an extra downstroke on a 'convenient' note instead of continuing the alternation, especially on string changes - but breaking the strict alternation is exactly what's most likely to cap your speed. The hand gets used to a predictable motion, not to remembering where a 'special' stroke is needed.
Both hands move in sync
The fretting hand needs to land the finger exactly at the moment of the pick strike, not before or after - a mismatch of a split second is heard as a smeared, unclear note, even with perfect pick technique. Synchronization needs to be trained separately from speed: at a slow tempo it's easier to hear exactly where the hands drift apart.
Start without the guitar, just the motion
Before adding notes, you can drill the pick motion itself in the air or over muted strings - down-up, evenly, with no notes at all. This removes the fretting hand from the drill and lets you focus purely on whether the pick's own motion is even.
Drill on one note, then a scale
Start alternate picking on a single note, repeating it with alternating strokes to a metronome - only once the motion is automatic should you move it onto a simple 4-5 note scale. A scale immediately adds the complexity of syncing with the fretting hand, so it's worth moving to it only once the alternation itself no longer needs conscious attention.
The common mistake: speeding up before it's stable
Alternate picking that's unstable at a slow tempo doesn't become more stable at a fast one - it just falls apart faster. Before raising the metronome, get the alternation sounding completely even, with no dropped strokes, at the tempo you're currently at.
Try it in practice
Open the metronome