Koinly supports a number of different blockchains via auto-sync so you can simply enter your public address (or xpub key) when setting up the wallet and Koinly will pull all your transactions from the blockchain.
What to do if Koinly doesn't support your cryptocurrency:
Create a custom wallet for your coin
Try to download a CSV file with your transaction history (from your wallet or an online block explorer) and import that to Koinly
If it's not possible to download a file then you will have to create one manually instead. See instructions for creating a custom CSV file.