The verb conjugates for 3nd person (he/she/it), so "have" becomes "has": "she/he has a trip". But when travelling, we actually say "she/he takes (or 'is taking') a trip", or "she/he is on a trip".
"He/she is having a trip" is gramatically correct, but 'trip' used this way sounds a bit slang, and may imply a drug-induced trip. So use "he/she is on a trip".
Or do you mean the person is falling over? :)