When pilots are ready to take off, we taxi up to the hold short line that separates the taxiway from the runway and announce ourselves. If it's an uncontrolled airport, we just have a good look to see that there is no one coming and then broadcast our intentions on frequency. At a controlled airport, we are announcing ourselves to the appropriate tower controller. Something like "Flight whatever holding short on bravo two," meaning that we're on taxiway B2. Some people just say "Flight whatever ready to go" and make the controller work out where they are.
The controller has many possible responses. He could say "wait," meaning that the airplane should stay where it is. (When they appear to completely ignore our call, the message is the same). Better is "taxi to position runway zero one," meaning that we can cross the hold short line and position ourselves on the runway in readiness for take-off, but still need to wait for a take-off clearance. Variations on that include "line up and wait," "position and hold," or "taxi to position behind the Navajo, number two for departure." You can see from the last that sometimes the controller lines up more than one airplane on the runway, so that they can be launched sequentially without the need to wait for each pilot to taxi to position. It can take a few moments as we don't want to go too fast, especially in high winds or with ice and snow on the runway.
The controller may issue the take-off clearance right away, even as we are taxiing up to the hold short line and haven't called yet. He's juggling arriving and departing traffic so that everyone gets the use of a runway, and no one cuts anyone off, even if an aircraft has to make an unexpected go-around. Sometimes the take-off clearance is modified with instructions like "short delay approved" meaning that it's okay to sit on the runway for a few moments, completing checklists, before applying take-off power and getting the heck out of Dodge. Sometimes the instruction is "cleared take-off no delay." If you require a delay on the runway then you must refuse that clearance, with something like "unable, holding short." The "no delay" clearance usually means that there is another aircraft on final approach to land.
This is all a long set up for something that made me laugh the other day. I'm on final and a little Cessna is "cleared take-off, no delay" from the runway I'm aiming at. He doesn't move for a moment, and I think he hasn't heard the clearance, but then he slooowwwwly taxies to position. The tower controller prods him off the runway in time for me to land, with "Papa Quebec Romeo, that's the slowest 'no delay' I've ever seen."