Keep climbing and following the Horse Heaven Trail posts. About two miles into your hike you may see three holes carved in the rock: these are mortars created by the Ohlone People to crush acorns, a staple of their diet. (It's possible to miss the mortars if you get off on a spur path).
Keep climbing -- the summit will be at your left the whole way. At about 2.3 miles in you'll reach a fence and a gate at the top of a ridge. Pass through it and head downhill for less than a hundred yards.
You'll reach a bog and need to rock-hop across it. Once you're on the other side, you're on the final ascent to the summit. Pass through the gate and follow more sign posts.
Eventually you'll reach a saddle with the summit at your left. The rest is obvious. Just watch out for mountain bikers on their way down as you head to the top, about a quarter-mile away. Vistas from the Mission Peak summit are simply awesome. Take a picture of the Summit Post to prove you were up there, rest up and rehydrate and prepare for the trip back down.