Start by getting your ally's base up to full saturation, and then ignore it and play as if you are on two base yourself. So immediately get your two-base tech and production up.
With the additional income, you will have a window of advantage because you can tech up more quickly than a normal game. To illustrate, for example you're zerg and your ally disconnects right at the beginning of the match. You will be able to build a spawning pool extremely fast with the additional income, making a 6-pool even faster than it already is normally.
So, play an aggressive game, keeping supply counts low and keep your opponents distracted. Do a stim timing, blink timing, etc. Stay in (or close to) battle, where micro is most important. This is your advantage being one player on the same economy as your opponents having to juggle armies. Two players controlling units in a single battle is not as efficient as one because you have a vision of your unit positioning, when to retreat, etc.
You can play on even footing until your supply maxes out. Your opponents can continue producing units while you're capped at 200. So, try not to get to that point and kill them first.