The best and cheapest way to travel is to get a low-fares airline flight to either of the following airports....
Barcelona; Girona; Toulouse; Perpignan; Carcassonne;
If you book early enough you can get very silly return fare prices !!
From Barcelona Airport there are at 4-5 coaches a day that go direct to Andorra (right up to Soldeu). From Toulouse and Gerona there are 1-2 coach connections per day to Andorra.
Otherwise you can hire a car from any of the airports.
Useful Links:
www.easyjet.com
www.ryanair.com
www.holidayautos.co.uk (for cheap car hire from airports)
www.andorrabybus.com (to book coaches from Barcelona, Toulouse or Gerona)
You can also (of course) drive down to Andorra. Andorra is about 10-11 hours drive from the channel ports. If you want to do this we can provide directions if required.
On Arrival in Soldeu:
Please ring either 00376 851059 or 00376 324139 (ask for Sarah) when you arrive in Soldeu to tell us of your arrival.
If you come by bus/coach then the main bus stop is about 300 meters from the apartment. If you are in a vehicle, you can park temporarily directly outside La Pleta del Soldeu on the main road.

Picture courtesy of www.soldeuonline.com