As you can see from the Google map, Chiswick BR station is a very short distance away. There are normally trains every 15 minutes from Waterloo, via Clapham Junction and Putney, but be careful to check South West Trains website for any weekend maintenence work and the service is often reduced or replaced by buses, causing significant delays.
Mortlake BR station is 10-15 minutes walk away, across Chiswick Bridge. You can also reach the Poly by buses 190 (from Richmond, Hammersmith, Ravenscourt Park and West Brompton tube stations, stopping on Great Chertsey Road), and the 272 (which terminates just outside the pavilion) or the E3 (to Chiswick station), both of which serve Chiswick High Road and are convenient for Turnham Green and Chiswick Park underground stations.
If you are using a satnav system, the postcode of the ground is W4 3UH .
South West Trains: Weybridge train from London Waterloo/Clapham Junction or London Waterloo train – Stop ‘Chiswick’.
TFL Bus Routes: 272 to Chiswick, Grove Park, (Bolton Road – Final Stop). E3 to Chiswick, Edensor Road (Chiswick Rail Station Stop).