Go to the eos.io website, scroll down to the bottom and click on the "get eos" button. EOS is an "erc-20" token so you will need an ethereum address to deposit the EOS. The address will have a public and a private key (two long alphanumeric codes). You send cryptocurrencies to your public key (address) and sign withdrawals with your private key. For Bitcoin, it is recommended that you only send from an address once because you expose your private key to the network when you send so you have to send the whole contents of the address. I don't know exactly how this works on the Ethereum network.
I don't know what happens on "eos.io" after you click on "get eos" because I am in the USA and they won't give the tokens to us. I had to buy some on an exchange called "Binance" and before I was able to buy eos on Binance, I had to buy Bitcoins and Litecoins on "Coinbase" using US dollars. If you buy eos on an exchange, you have to register your address with eos.io or they will become worthless after June 1 when the eos network instantiates. Alternatively, you could sell your eos before June 1 or wait until after June 1 to buy them.
You can get an ethereum address at www.myetherwallet.com and you will probably want to use a browser plugin called "MetaMask" to manage your private keys. I only use MetaMask now because it allows you send and receive and generates public and private keys for you. You can learn about it at metamask.io.
Once you have a public key, you can check up on its contents in metamask on your browser or at etherscan.io. Etherscan.io lets you track Ethereum and ERC-20 transactions. It also has lots of information about the different coins including the Token Contract Addresses that you need to add token types to MetaMask.
I just learned about all the Ethereum, ERC-20 and wallet stuff last weekend and am a new-comer to it so take my explanations with a grain of salt. I've been using Coinbase to buy Bitcoin, LiteCoin, and Ethereum for about 8 months. I hope that this info will point you in a right direction.
Thanks for being helpful. I love to see this. :)
@smarmy thanks so much.... It was really helpful