Ok I've downloaded Electrum and put the wallet address I sent the coins to and they have appeared in there. I'm not sure what I do next though, do I need to use the private key from my sending account, or the receiving Ledger wallet? the sending is through Coinbase so I'm not sure how I even got about getting the private key from there (if at all available)
Click on receive in Ledger. You should get a bitcoin address. Copy this and paste into Electrum "Pay to" box. Send the amount from Electrum and you should receive it instantly in your Ledger. Do not mess with the private keys.
Ok thanks i'll try that. Does it matter that the wallet address changes each time and doesn't match up with where the initial transaction was sent?