What's the best way to patch up after a fight?

Apologise. Doesn't matter how, what, why, when or who said what -- apologise and move on from there. For me personally, if I initiated the fight, I would naturally apologise (but reluctantly haha). If he started it and he apologised, I would also apologise because I would have definitely said some horrible things during the fight in retaliation. After the apologies are out of the way, things are always easier. We'd always end up cooking a meal together (because arguing works up an appetite) and we settle down to watch our favourite series.