The only way to get to know a professor is to sit in the front row of class every day. Also, get to know the T.A.'s. You spend more time talking with them, and they know you well enough to help you. Don't put off writing your papers. I learned this the hard way.
Problems can arise at the last minute.
For instance, your computer might break down. When I get a writing assignment I make copies of the articles that pertain to the topic of my paper, I highlight important information, and write notes in the margins of the articles. Then I compile all the information and begin my outline. I am the Queen of Procrastination, so I thought the best idea would be to take advantage of the services offered at the Writing Center, in Burnham Hall. As soon as I get a topic, I go to the Writing Center and start brainstorming with an adviser there.