South Western Railway operates a train from Woking to Egham 3 times a day. Tickets cost $7 - $12 and the journey takes 23 min. Alternatively, you can take a bus from Woking to Egham via Elmsleigh Bus Station in around 1 h 6 min.
From Woking train to Egham. 23 min £7. From Woking Railway Station bus to Elmsleigh Bus Station then bus to Egham, Langham Place. 1 h 6 min £8. From Woking taxi to Egham. 16 min £56. From Woking drive to Egham. 16 min £2.