Liddes is connected to Martigny several times a day by public transport. From Geneva airport you have every 30 minutes a train to Martigny. From Martigny you take a train to Orsières and then a bus to Liddes.
Use 'Liddes' when you type in your destination point in the travel website www.sbb.ch
IMPORTANT: When you type in Liddes, select the one where it only says Liddes, nothing before or after that word.
Another option to buy tickets is the omio app
You will recognise that you are at the right stop as you come into Liddes, pas the fuel station Tamoil and stop next to the tourist office and the Raiffeisen atm.
If you come from Aosta Italy, there is 1 bus max once a day or hitchhiking. https://aosta.arriva.it/en/aosta-martigny/