first thing you'll need to enter the Crypto world is a wallet  here's a list of known wallets and their comparison: https://www.cryptocompare.com/wallets/#/overview

Once you chose the coin you want to buy and  setup a relevant wallet you'll be able to send and receive Bitcoin/Altcoins. easiest way to buy Bitcoins by creating a wallet on Coinbase.com , there is also localbitcoins.com and paxful.com where you can buy bitcoins using different methods (you'll need the address of your wallet to transfer the coins you bought of course)

once you got the wallet and the coins, you can now invest in ICO of your choice, how to contribute in an ICO is different, they usually provide instructions on their website, you can monitor newly released ICO's on websites like https://cointelegraph.com or https://www.coindesk.com or even here on http://bitcointalk.org

You need to be careful with ICO investment because its risky as you're basically giving your money to people you don't know and with no guarantees.. you should research the business and team carefully first and be comfortable its a profitable model