First, let me explain that ERC20 tokens are designed using the Ethereum Blockchain, they do not have their own blockchains, this means that they are essentially compatible and able to be sent to an Ethereum Address.

This is convenient because now you can easily store these tokens in a much safer wallet than say leaving them on an exchange.

Here’s how to quickly and easily determine if a coin is an ERC20 token.

You can use Etherscan.io, or ethplorer.io.
These sites are pretty similar to each other in that you can use the search bar to type in the name of the coin you’d like to investigate.
If it is spelled correctly and shows up as an option then you know it is an ERC20 token.

Now if you have purchased some ERC20 tokens and you’d like to store them in a safer wallet:

You can generate a new Ethereum address using MyEtherWallet.com or MyCrypto.com.
At the moment, these sites are pretty much identical and serve the same purposes.

Keep in mind that you can and should disable your Wifi and disconnect your device entirely from any internet connection to further ensure your security from hackers BEFORE you type in your password to begin the setup of this wallet.

As always, when you create a new wallet:

• Choose a very strong password
• Always backup the private key and the keystore file

When it comes to accessing wallets that you’ve generated in this way, the better way to access your funds is by using your Keystore file rather than inputting your private keys, since your keystore file is protected by that super strong password you created.

If all you want to do is check the account balance, this is safely and easily done by going to etherscan.io and inputting your PUBLIC address.

Ok so you’ve got the wallet set up, and you’re ready to send over your tokens to this newly created wallet.

• Access your wallet using your Keystore file and password, again, you should disable your wifi for this part.
• Locate the Account address. This is your public key. This is the address to which you will send your ERC20 tokens.
  (It is up to your own discretion how many different tokens you want to store on a single wallet.)

Once you’ve received confirmation that the tokens have been moved, they will not be visible in this wallet right away.

You’ll need to locate the orange “show all tokens” button.

Unless your tokens are brand spankin’ new, most likely they will be included in this long list.
If you find the name of your token on this list, click on the “click to load” option. After a few moments you will see your token balance. If you want to move these tokens again, all you need to do is find the dropdown menu next to the “amount to send” option to select the tokens you’d like to transfer.

If you cannot locate your tokens on that long list I mentioned earlier, don’t worry, there’s an easy way to add them to your wallet yourself.

You’ll need to locate the token’s contract address as well as it’s symbol or official abbreviation and the amount of decimal places.

A really easy way to find the token contract address is by searching the token’s name on ethplorer.io or etherscan.io that search will show you all of the information needed to fill out this form.

In the case that your token has had multiple contract addresses, find the correct one for your tokens by searching your public key,(the one where your tokens are stored before you move them onto your newly created wallet.)
Search this address on etherscan.io to find the correct token contract address and use that to fill out the custom token form.

A very important thing that you should also know: do NOT send any tokens to their contract address, these tokens will be lost.

There is a new EIP, or Ethereum Improvement Proposal in the making that will prevent you from doing this, but as it stands right now if you send your tokens to the contract address they will not be able to be recovered.

Additional Reading/Links:

Etherscan
Ethplorer
MyEtherWallet
MyCrypto
New EIP