By Tube
This is a large district and it is served by a similarly large number of tube stations:
South Kensington District, Circle and Piccadilly lines. For the museums.
Knightsbridge Piccadilly line. For Harrods, Harvey Nicholls and other upmark stores.
High Street Kensington District and Circle lines. For general shopping and Kensington Gardens.
Hyde Park Corner [Piccadilly line). For Hyde Park.
Sloane Square District and Circle lines For King's Road.
Earls Court District and Piccadilly lines.
Kensington Olympia District line.
West Brompton District line.
By bus
Like most parts of Zone 1 Central London, this area is well connected by a variety of bus services. Here is a general list of the bus routes serving each major destination in this area:
South Kensington Museums: 14, 49, 70, 74, 345, 360, 414, 430, C1
Knightsbridge: 9, 10, 14, 19, 22, 52, 74, 137, 414, 452, C1
High Street Kensington: 9, 10, 27, 28, 49, 52, 70, 328, 452, C1
Sloane Square: 11, 19, 22, 137, 170, 211, 319, 360, 452, C1
King's Road Chelsea: 11, 19, 22, 49, 211, 319
Earl's Court: 74, 190, 328, 430, C1, C3
Hyde Park Corner: 2, 9, 10, 14, 16, 19, 22, 36, 38, 52, 73, 74, 82, 137, 148, 414, 436, C2
The most useful buses for visitors to this area are:
9, from Aldwych via Trafalgar Square and Piccadilly Circus serving Hyde Park Corner, Knightsbridge, Royal Albert Hall, and High Street Kensington to Hammersmith
10, from King's Cross St. Pancras and Euston Station via Oxford Circus/Oxford Street and Marble Arch serving Hyde Park Corner, Knightsbridge, Royal Albert Hall, and High Street Kensington to Hammersmith
11, from Liverpool Street Station via the City of London, St. Paul's, Aldwych, Trafalgar Square, Westminster, and Victoria Station serving Sloane Square and King's Road Chelsea to Fulham
14, from Warren Street Station via Tottenham Court Road, Shaftesbury Avenue/Soho, and Piccadilly Circus serving Hyde Park Corner, Knightsbridge, South Kensington Museums, and Fulham Road to Fulham and Putney
19, from Finsbury Park and Islington/Angel via Tottenham Court Road, Shaftesbury Avenue/Soho, nad Piccadilly Circus serving Hyde Park Corner, Knightsbridge, Sloane Square, and King's Road Chelsea to Battersea
74, from Baker Street via Oxford Street and Marble Arch serving Hyde Park Corner, Knightsbridge, South Kensington Museums, and Earl's Court to West Brompton, Fulham, and Putney
211, from Waterloo Station near South Bank/London Eye via Westminster and Victoria Station serving Sloane Square and King's Road Chelsea to Fulham and Hammersmith
C1, from Victoria Station serving Sloane Square, Knightsbridge, South Kensington Museums, Earl's Court, and High Street Kensington to White City/Westfield London
Note that all of these routes use iconic London red double-deck buses except C1, typically operate at least every 10 minutes, and that any travelcard pass is valid for all buses otherwise, buses are £1.30 per boarding using Oyster pay-as-you-go.