The diagram to the right shows standard traffic patterns for an airport with two parallel runways. There are 5 parts to the traffic pattern:
Departure (sometimes called upwind)
Crosswind
Downwind
Base
Final
Note that the pattern also has a direction (left or right) defined by the direction in which all the turns are made. In the diagram to the right, the runway on top is a left hand pattern, while the runway on the bottom has a right hand pattern.
The standard pattern is always left traffic, but various factors (like parallel runways) may cause a runway to use right traffic. This will be listed on the chart and in the chart supplement. The tower controller can also determine which pattern direction to use.
The standard way to enter the traffic pattern is at point 1, on a 45 degree to the downwind. However, as tower you may instruct an aircraft to proceed direct to any point in the pattern. If not joining the downwind, entering a (left or right) base or direct to final ("make straight in") are the other typical entries.
The standard way to exit the traffic pattern is at point 6, either straight out or on a 45 degree offset. However, as with the entry, as tower you may instruct an aircraft to exit from any point in the pattern.
Source: Aeronautical Information Manual (AIM) Chapter 4
VFR departures should get four pieces of information:
Instructions for exiting the pattern (what leg of the pattern to exit on)
The current wind
The runway they are using (and the intersection if they're not at the end)
Cleared for takeoff.
Example: "Cessna 123AB, make straight out departure, wind 110 at 7, runway 13R, cleared for takeoff."
Arriving aircraft will contact the Tower when they are 5 to 10 miles from the airport, and they should give you their position and intentions (such as, "11 miles northwest, inbound for landing," or "over Forest Grove, inbound for touch and goes"). Again, you won't be able to tell who is who, because all aircraft squawking 1200 are just identified with a 'V' on the CRC STARS screen, along with their Mode C altitude. Based on their position, you should give instructions on how to enter the traffic pattern and when to call again. Something like "Proceed direct to left downwind runway 13R, report midfield," or "Make straight-in to Runway 2, report 2-mile final."
The tower controller will issue one of the following clearances to aircraft arriving at the airport.
Full stop - A regular landing clearance, aircraft will touch down and exit the runway. "Cleared to land."
Stop and Go - A/C will touchdown and come to a full stop. Reconfigure and take off again. Use cautiously, you are giving the aircraft permission to remain stopped on the runway for an unspecified amount of time.
Touch and Go - Aircraft will touch down, reconfigure for takeoff, and take off again without coming to a stop.
Low Approach - Aircraft will make the approach, but will not touch down.
The Option - Allows aircraft to perform any of the preceding maneuvers. In circumstances where a certain procedure is not available due to operations (i.e., other aircraft in the pattern, so you don’t want to allow a stop and go) "Cessna 123AB, wind XXX@XX rwy 13R, cleared for the option, stop and go unavailable."
Make Short Approach - Not a clearance, but an additional instruction used to expedite an aircraft's base leg to clear the path for other traffic- i.e., pattern traffic turns base as approach hands off an IFR arrival on a 9 mile final. "Cessna 123AB, make short approach." Pilots may also request short approaches for training purposes, which you may accommodate if traffic permits.