Okay so you are at a networking event and you have decided to have a drink while networking. Good for you. Here is something to remember:
Hold your drink in your left hand.
Why? Because you are going to be shaking hands with your right and few people want to shake a hand that is cold and wet from holding a drink! Sure you can always wipe your hand on your pants or dress but what kind of impression does that make?
In any situation other than a beach party or barbeque, drink your beer from a glass. Seriously, a bottle or a can is okay for informal situations with friends but for situations where you are making a good first impression, use a glass.
In general, white wine glasses are held by the stem so that the wine remains chilled as long as possible. Red wine is often cradled in the hand as it is usually served a room temperature.
If you are drinking mixed drinks, I like to avoid drinks that have celery sticking up out of them (e.g. a Caesar), toothpicks of any kind and I also quickly discard any garnish that the bartender may have put on the rim. Why? Drinking around these things is often awkward and sure as shooting, the last sip you take will cause that slice of orange or lemon to slip off the rim of your glass and onto your shirt. Who needs that?
It is also a great practice to stage your drinks so that you have one alcoholic one and then a non-alcoholic one. If the party you are attending is likely to go on for three to four hours you could easily find yourself drunk before the night is through and rarely does such a thing result in great networking. (Keep in mind you may think it is great while in that state but others...not so much). If you are concerned about appearing like the only one who is not there to party, just ask the bartender to reuse your glass. So if you are drinking rum and coke, then the next refill is just coke. Who is to know?
Often when you are served a drink you will be given a cocktail napkin at the same time. I usually just drop this in the trash but I have seen people use it to wrap their drink and keep their hands from getting cold and wet. Of course, since you are using your left hand this is not an issue for you.
If you are drinking try to position yourself next to a table or ledge where you can put your drink down while you are getting out your business cards etc. It isn't going to be great to put it on the floor and asking the other person to hold it while you dig out a business card is less than ideal. It is a great idea to have a few business cards stuck in a suit coat pocket for the evening so that you don't have to extract one from its case but you are not always going to have that luxury.
Caution, caution caution. I recommend forgoing the appetizers if you are serious about networking. It is almost impossible to do both well. Some of these little snacks are one bite wonders so they can be popped into your mouth to keep you from keeling over in hunger but let's face it - if they are serving such things it is likely a pre-cursor to dinner and there will be enough food to go around.
Again if you must eat - try to pick simple snacks that are not messy and that preferably can be done away with in one or two reasonable bites. Pizza for example is not a good idea. I also try to avoid anything that has a toothpick, wrapper or other item that I must dispose of although this can be hard to get away from.
It is also a great idea to have a napkin handy any time you are eating food and networking. Eventually you will find yourself with messy fingers and who exactly is going to want to shake hands with you then? Licking your fingers is not going to resolve that issue either! If you do end up with a mess on your hands, just apologise to the person standing there with his hand out and mention that your fingers are not in a "good condition" to shake hands and then get on with your conversation.
Don't do this.
Seriously, if you are at a party with friends, go for it but if you are at an event to network - this doesn't work well at all. Just trust me on this - don't attempt to eat, drink and network at the same time. You don't want to talk with your mouth full and you won't have a free hand to shake. Any free hand you do have to shake will be either wet or greasy. I won't say any more. Don't do this.