La Gomera cannot be reached directly by air from the European mainland. The journey to La Gomera generally consists of:
A flight to Tenerife-South, to the airport Reina Sofia (TFS).
Ferry journey to La Gomera.
Transfer on the island to your accommodation (20 minutes in the case of Apartments Los Telares).
You might want to consider a transfer company. Autobuses Mesa arranges everything from you concerning your arrival / departure, including ferry tickets.
If you are landing in Tenerife North Airport, as it is well connected with most spanish cities, and some european countries, you might want to take a flight to La Gomera. The plane trip length is of 35 minutes from Tenerife North to La Gomera. Binter Canarias is the only company currently making that trip.
From Los Cristianos seaport in Tenerife there are two companies, Fred Olsen Express and Naviera Armas, that have daily trips to La Gomera. Both companies websites allow to make your reservation online as well as check their schedules. The trip lenght average is about 50 minutes. Los Cristianos seaport is 12 Km away from Tenerife South Airport, and 75 Km. away from Tenerife North Airport. From TFS (Tenerife South Airport) it takes around 15 minutes to get to the Seaport. You can either take a taxi for around 22€ or the regular bus for 2€/person. Check the Airport website for lines, pricing and timetables.
Shipping companies also have free bus connection from the Santa Cruz Bus Station (10 minutes away from Tenerife North Airport). You can buy your tickets including the ferry-bus in the station, as both companies have offices there. The advantage is that this way the ferry will wait for the bus to arrive before departing, so you will not miss your trip.
Getting around on La Gomera
When in La Gomera, the main towns are communicated with buses. You can check the timetables here.
Public transportation is unefficient if your aim is to tour around the island, as many of the touristic spots are outside the bus routes. Of course, it is part of the adventure to use bus lines to reach the head of the footpaths, but you have to be very organised for that. You shall rather hire a taxi to take you and pick you up after your daily route. Some trekking routes can take around 5 hours to complete, so you have enough for a day with a single path. This option gives you the freedom to explore the footpaths of the National Park.
If your intentions include less trekking and more relaxing, you might find that the best choice is to rent a car or bike. Car rental companies have very competitive prices. Fuel is also very cheap, so the overal cost will not be much. They have offices in most hubs, specially around the Seaport of San Sebastian. Here is a list of some rental companies operating in the island:
Traveling time summary:
From TFN (Los Rodeos Tenerife North Airport): 15 minutes (TFN - Bus Station in Santa Cruz) + 1 hour (Ferry-Bus from Bus Station to Seaport of Los Cristianos, direct line) + 50 minutes (Ferry from Los Cristianos to San Sebastian) + 25 minutes (San Sebastian to Hermigua) = 2:30 hours.
From TFS (Reina Sofia Tenerife South Airport): 15 minutes (TFS - San Sebastian Seaport) + 50 minutes (Ferry from Los Cristianos to San Sebastian) + 25 minutes (San Sebastian to Hermigua) = 1:30 hours.