Create a key and test its adequacy on a sample of problems or papers. Check your system of assigning points, especially partial credit, with a faculty member and/or other graduate student teachers. If multiple graduate students are dividing the responsibilities, check that everyone would assign the same grades to a small sample of assignments.
Grade question by question, rather than student by student, for homework and exams. For essays, you may want to read and comment on each of the introductions before reading all the papers.
Shuffle the exams or papers between questions. Reordering them avoids a pattern of becoming systematically harsher or softer when you get to the bottom of a pile.
Annotate your key. That is, note how much credit was given for specific errors as you go along. Sorting similar errors into piles reduces the time to find comparable papers.
Avoid grading when you are extremely tired or have difficulty concentrating. Your comments will be more ambiguous and your grades less consistent when grading under these circumstances. Grading will also take longer.
Examine the overall class performance for patterns. Especially for exams, tabulate scores on each question to analyze where student performance was weak and/or where questions were ineffective so that you and/or the professor can respond to problems. You might want to consider providing a handout to explain key concepts that were missed by students on their exam answers.