I'm using a bright color of thread for better visibility; when doing this for real you'd want a thread that matches your sequins and/or fabric.
What you need:
Loose sequins - flat or cupped
Beading needle (most regular hand-sewing needles won't fit through seed beads)
Seed beads or tiny crystals (optional)
Thread conditioner or plain beeswax to keep your thread from tangling
Regular sewing thread or beading thread (your preference)
Step 1: Simple overlap stitch
This gives the same look that you get from pre-strung sequins.
Bring the needle up through the fabric and string one sequin. If you're using cupped sequins as shown, you can choose to have the cup facing up or down (it's personal preference and what effect you want). Some people find cup-side-down snags less.
Take the needle back down through the fabric just beside the sequin (stitching one side of the sequin down), and then come back up very close to the edge. String another sequin through the center and repeat. The overlap will cover your stitches and hide the thread.