Try not to read too many exams or papers in one day so that you don't get mechanical. Meet with other TAs to grade sample exams or papers and to address problems. Many TAs recommend reading a paper a few times. The first time, read through it quickly, to see how it generally reads. The third time, write your comments and assign a provisional grade.
Judge papers primarily on content, organization, and style.
Grades are relative. Try to think about the papers in relation to each other. Try to rank them, from strongest to weakest. The only way to be fair is to be consistent. Be as specific and constructive as possible.