Having a game plan or a process in mind for how you will deal with certain conversations that you have is a good way to ensure that you will make the most of that conversation for the long term. This is a suggestion only for meaningful conversations in the business or career realm. I don't think you have to have a process in place for every conversation that you have although I am not saying that you can't.
The first thing to make sure that you do is to leave the conversation that you are having with a specific course of action for follow up. Letting someone know that you liked what they had to say and that you would like to connect. You can schedule a time to do that right then and there (not as likely as people don't always carry their schedules around with them) or you can let them know that you will be giving them a call and then get a rough idea from the other person when a good time may be. This doesn't have to be specific it can just be a range or a block of time. Setting this up ensures that you will actually do it and it sets it up in the other person's mind as well to be expecting a call.
The second course of action is to make your follow up immediate. Don't wait a couple of weeks to follow up with someone. In this day and age we have access to so many more people that it becomes difficult to remember everyone that we talk to. This is especially important at networking events where you are exposed to hundreds of people. In this case it's not OK to use the method from the movie Swingers and wait 5-7 days to call the person that you just talked to.
Now that you have followed up immediately, the last thing you need to do is speak with clarity and confidence. Make sure that you articulate clearly what conversation you had with that person and what your idea was for the relationship going forward. It's probably a good idea to take notes during times where you are having conversations with multiple people so that you can write down key phrases and ideas from the conversation that you can reference later. By doing this, you make yourself more memorable to the person on the other end of your conversation and sound more sure of yourself as well.
Having a solid follow up process is key when you are having conversation and building relationships. Without it, you are wasting your time. What ideas have worked for you in the past when following up with people? What success have you had a result of your follow up efforts?