The first step to Getting Things Done is writing everything down (also known as capture). Unless you are unusually unbusy or focused, you will forget things that must be done. So capturing these items is essential, especially before they slip the mind, or when the process becomes less fresh. The latter is especially important with repeated tasks and projects. For the college instructor, there are lots of common tasks that get repeated at the beginning of each semester (photocopy the syllabus, check on the room if it is a new room assignment, prep Blackboard, and so on). Making notes as you go through this process is fairly easy and priceless, as it will seem unfamiliar after a summer out of the classroom.
A system of writing down items is not helpful if there's not a way to access those items later, especially at the right time and place. There are several ways to achieve this. One is to simply revisit your lists, constantly checking, marking, and editing; this is the paper and pen method, and is terribly laborious (I remember trying this 15 years ago with a DayTimer). Another method is to process items according to context, project, date, and priority. Thus, things you can only do on campus (such as photocopy the syllabus) are assigned the campus context, and when you are on campus you check that context and can see all the things you should do. This can be done with pen and paper, but again is terribly laborious, with lots of rewriting and marking.
GTD applications are so useful, especially in comparison to paper and pen systems, as you can tell the app to play it forward (as Merlin Mann has called it, sending a message to your future self) and show that item in, say, one month, or a year, whatever. It's the ultimate tickler file; the item or project is made to disappear and then reappear at the right time and place. It can be made to repeat (check the car's tire pressure once a month, upon completion). This can be done quite easily with OmniFocus and Things. For Things, items are scheduled to happen on a certain day; when that day arrives, the item bubbles up. With OmniFocus, items are given a start date.
Another method is, with OmniFocus, to flag items. Then the Flag view shows you all the flagged items. These might be items you want to complete today or this week, items that have priority, or tasks you promised to do for someone else. The flags are fairly open to interpretation. With Things, the Today list is where tasks are moved so that they stand out (this is closer to the David Allen GTD system).
Tasks can also be given a due date, which highlights them in either an angry red or irate orange. These tasks will then stand out so that they are not missed.
In the end, however, you oddly have to return to checking all your lists, in what is called the review mode of GTD. All lists need to be read through, checked, and updated. It's always interesting to see how many things have either been done, or are no longer applicable, as you read through everything. But this is key, as items can be missed, mislabeled, need changing, or require additional tasks. So reviewing is critical for any system.
At its heart, GTD is writing everything down, and then finding ways so that the system bubbles up what you need. The secret sauce is this bubbling, so that the frail human memory can recall what is needed. Many find the start date/scheduling to be the best method for this bubbling up, but the other methods of flagging, due dates, and review are also essential.
Capture, schedule, flag, and review. Good luck.