By air: Murtala Muhammed International Airport (LOS) in Ikeja is the main entry point, with direct flights from most of West Africa, the Middle East, Europe and a handful of US cities. The international and domestic terminals are about a kilometre apart and you change buildings to switch. The airport is on the mainland; transfers to Victoria Island take 45 minutes in clean traffic and well over two hours in evening rush. Pre-book a transfer; do not negotiate with the touts in the arrivals hall.
By road: the main land entries are from Cotonou (Benin) in the west (the bus journey is about three hours plus border, with delays unpredictable) and from Ibadan in the north (about 2.5 hours on the toll road). Long-distance buses arrive at chaotic motor parks at Iddo, Ojota, and Mile 2 — and from there you take a taxi.
By boat: there are scheduled ferries from Cotonou to Lagos Lagoon but the route is intermittent and used mostly by locals.