The 29 tours we sell that stop at Hallgrímskirkja leave from Reykjavík and Keflavík Airport. Most of them start in Reykjavík, so for anyone based in the capital there is nothing to arrange beforehand.
20 of the 29 collect you from your accommodation or a designated stop, so the tour is the transport — there is nothing else to arrange and no timetable to read.
A seat on a day tour here starts at €40 and typically runs €101, per person, private charters excluded because those are priced per vehicle and would flatter the figure. There is also a scheduled bus or transfer serving Hallgrímskirkja, from €95 — cheaper than a tour, with no guide and no stops on the way.
The days themselves run from about 1 h to 6 h 30 min door to door, so check the length as carefully as the price — the cheapest seat is often the longest coach day. 11 different operators run here, which matters more without a car than with one: if the weather cancels your day, there is usually another departure rather than a lost trip.
Being driven is the easy answer here: enough operators run it that a cancellation rarely loses you the day, and you get to look out of the window instead of at the road.
Cheapest way in without a car: a guided day tour from Reykjavík, from €40 per person.