Don't make threats and give ultimatums. Unless you are actually prepared to carry out these threats and ultimatums they will lose any power to influence the drinker. In fact, they may even provide an excuse for drinking, especially if there is a pattern of drinking to avoid stress and painful circumstances. Therefore you could be left feeling even more frustrated than before.
Don't cry and sulk and withdraw to punish the drinker. The drinker can again view his as behaviour best avoided by getting drunk, perhaps with the immortal words "No wonder I drink, look at you!".
Don't try and have a meaningful conversation about the drinkers behaviour or your lives together when the drinker is intoxicated. It is easy to get lured into a conversation - don't. Wait till the morning or when they are sober.