Hour angle H = LST − RA. Then sin(alt) = sin(δ)sin(φ) + cos(δ)cos(φ)cos(H), and azimuth comes from atan2(−cos(δ)sin(H), sin(δ)cos(φ) − cos(δ)sin(φ)cos(H)) measured from north through east. Sidereal time gains about 3m56s per day on civil time, so LST must be recomputed for your actual observing moment — it is not the clock on the wall. Refraction is not applied; near the horizon the true altitude is a little higher than computed.