There are many forms that you will need to deal with as a graduate student. Most forms can be found online. The best way to process forms is typically in electronic form, delivered via email.
Many of these forms require the signature of two sets of people: (1) your advisory committee members (including your advisor) and (2) the GD, the Department Head, the College Dean, or the Graduate School. The fastest way to get these forms signed is to get the signatures of people in set (1), then send them to the GC, who will see that the appropriate signatures from set (2) are obtained. If appropriate, the GC will have you deliver them in person to the Graduate School once completed, but this is rarely necessary.
It is almost never appropriate to send a form directly to the GD or DH, even if the form indicates the need for their signature. Decisions related to plans of study, admissions, transfers, etc. are always made initially by an advisor and then forwarded to the GD/DH for approval. If you send a form directly to the GD/DH, you can be sure that you have just slowed down the process.
On occasion you will want to discuss the contents of a form with the GD, in which case a personal meeting or email exchange will be appropriate. If you only need a signature from the GD, it is far more efficient to leave the form with the GC than to try to locate the GD personally.
While the GC will make every effort to obtain the signatures as quickly as possible, sometimes one of the necessary people will be out of the office for several days. So it is important to turn in forms well in advance of any deadline you may be trying to meet.
In addition, there are many dependencies in the forms that students must fill out. For example, international students should have a Plan of Study approved before they go on Coop or Internships (see Internships and Co-ops). Also, application for exams require a Plan of Study already on file. It is important that students pay attention to the deadlines and milestones required for their progress. Submitting all forms at once will not get them done any faster and at times it might actually slow down the approval process.