I'm confused with the usage of "sign up", "apply for", "register". Which of the following sentences is acceptable?
Please give examples of each verb phrase.
1. I'm looking forward to the one-day trip to Keelung.
2. I'm willing to apply for the trip.
3. I'm willing to sign up the trip.
4. I'm willing to register the trip.
Use "apply" for something where you might get rejected. Like you "apply" to a university for admission. Or you apply for a credit card from a bank, or for a visa to visit a county.
"Register" or "sign up" are for activities or reservations. "Sign up" is more informal. You might register with the hotel to take the 6AM shuttle to the airport.
(And all the words take a "for" in your examples. Sign up for, register for, apply for.)