Several companies offer organized day tours of Upolu from Apia. Prices vary according to the number of participants, whether you travel by private car or minibus, if lunch is included, etc. Don't expect much "narration" from the guide—it's mainly a way of getting around. The tours don't operate unless at least eight people sign up, so ask about that, and if it looks doubtful, check elsewhere. Even if organized sightseeing isn't your usual thing, the convenience and price makes it worth considering here. If nothing if happening, consider hiring a taxi for the day.
Samoa Scenic Tours, at Aggie Grey's Hotel, has an afternoon tour around town or a morning trip to the Piula Cave Pool. Full-day trips are to Lefaga's Matareva Beach, Aleipata, or Manono Island. The full day tours require a minimum of three or four participants while the half day tours can be scheduled anytime.
Jane's Tours at the back of a mall on Vaea St. offers full-day trips to Aleipata on Wednesday and Saturday, and Paradise Beach on Thursday. The Manono trip on Tuesday.
Samoa On Foot does hiking tours to Lake Lanoto'o at S$50 pp including hotel transfers, rubber boots, and raincoats. This is the easiest way to do the lake by far and their local guide Eddy knows the area better than anyone on earth. Samoa on Foot also organizes hikes to the PeaPea Cave in O Le Pupu-pu'e National Park with the final descent into the cave via a rope.
Oceania Tours in Apia has a variety of overnight tours to Savai'i and American Samoa.