By plane:

Spain:
Barcelona airport (all day bus and minibus services run from the airport, also car-hire)
Aeroport de Girona airport (connection to Barcelona by train and bus, car-hire)

France:
Toulouse airport (regular minibus and bus service)
Perpignan airport
Aeroport de Caracassonne airport (train or bus to Toulouse)

By train:

Spain:
Madrid-Lerida. Connection by bus to La Seu d'Urgell then bus or taxi to Andorra
Barcelona-Puigcerdà. Connection by bus to La Seu d'Urgell then bus or taxi to Andorra l'Andorre.

France:
Paris-Toulouse - Ax les Thermes or l'Hospitalet and connection by bus to Andorra. For bikers there is a night train form Paris to Toulouse that you can stuck the bike on and get some sleep in a bed.
Perpignan-la Tour de Carol and connection by bus to Andorra.

By Road:

Spain:
Madrid-ZaragoZa-Lerida-Pons-Andorra (613Km - regular bus service 3 times a week
Barcelone-Andorra (regular bus service all day and taxis):
- via Cervera (208 Km)
- via Solsona (196 Km)
- via the Cadí tunnel (185 Km-peage) *recommendedé
Lerida-Andorra (141 Km)
Tarragona-Andorra via Tàrrega (210 Km)
Girona-Olot-Puigcerdà-Andorra (219 Km)

France:
Paris-Toulouse-Foix-Ax les Thermes-Andorra (882 Km)
Marsella-Narbonne-Perpignan-Bourg Madame-Andorra (757 Km)
Biarritz-Pau-St.Gaudens- Foix-Ax les Thermes-Andorra (451 Km)
Toulouse-Andorra (196 Km - regular bus service)
Foix-Andorra (55 Km)
Perpignan-Andorra (128 Km)