To get the airdrops they need a wallet. Most of the airdrops are ERC20 Tokens. So you can use your ETH address. Make sure you have the private keys. Do not use exchanges eth address.
To create a new wallet Go to https://www.myetherwallet.com/
Make sure the https is there and it says MyetherWaller Inc US.
Enter a password and create a new wallet. You can download the JSON files which contains the keys to your account. Store the file at a safe place.
You need to share the public address to airdrop sites. DO NOT Send the private keys.
To track your account balance and tokens you can use https//ethplorer.io/
For those who actively search for cryptocurrency airdrops can use this Website: http://coin-updates.com/intro
In coin-updates scroll to new airdrop sites. Click on register, Complete task and enter erc20 token address. Wait for the airdrop. :)