Begin by coiling the leads of your LEDs with pliers, remember that the cathode of your LED has a flat indent on it.
Sew two "rails" into your project - one for ground and one for positive. Embroider connection pads into your fabric, 3 or 4 stitches in the same place should be enough.
Pin your LEDs into place, and sew them onto your fabric. This is when it is important to use two needles at once, so you may continually test the circuit whilst it is being constructed. I use a 9V battery to test, because both connection points are on the same side, and I can just hold the battery to connection pads I sewed in when I started. You shouldn't use a 9V battery to power the circuit though, as you will burn out the LEDs.