James has (gone/went) to the airport to pick up his father.

Step 1. The verb following have is a form of go.
Step 2. Go is an irregular verb.
Step 3. Choose the past participle form, gone.

Step 1. The verb following have is a form of take.
Step 2. Take is an irregular verb.
Step 3. Choose the past participle form, taken.

Step 1. The verb following have is a form of come.
Step 2. Come is an irregular verb.
Step 3. Choose the past participle form, come.

Step 1. The verb following have is a form of see.
Step 2. See is an irregular verb.
Step 3. Choose the past participle form, seen.

Step 1. The sentence does not contain have, so a simple past tense form can be used. Brought is the past tense of bring. (Brung is a nonstandard form and therefore should not be chosen for edited written English.)