If you're driving to Dulwich, you can take the A205 (South Circular Road) and turn onto Gallery Road (B221) or take Lordship Lane (A2216) and turn onto Dulwich Village (B269). If you're traveling by train, you can take a train to Dulwich station from London Bridge or Victoria stations.
If you're coming from other local landmarks, such as Crystal Palace Park, you can take the P13 bus or by train from Crystal Palace station to Sydenham Hill, then walk to Dulwich. From Clapham Junction, you can take the Southern Rail train to North Dulwich station. From Brixton, take bus route 3 or 37 to Dulwich Village or Forest Hill and then take the P4 bus.
The closest airport to Dulwich is London City Airport, which is about 10 miles away. It's a relatively small airport, but it's convenient for travelers heading to Dulwich or other parts of London. From the airport, you can take public transportation or a taxi to reach Dulwich. The quickest route is to take the DLR to Canada Water, then transfer to the Jubilee line and take it to London Bridge station. From there, you can take the Southern Rail train to either North Dulwich or West Dulwich station, depending on where you need to go.