This process is very simple. First, select an exchanger Like Bittrex, Binance, Hitbtc, Forkdelta or idex. Deposit Bitcoin or ETH in that exchanger to buy altcoins. Select good coin and that price is presently low, hold or wait few days and decide to sell when you see profit.
Don't start your trading with Hitbtc because they will charge a very high fee, So my suggestion is to register in Binance and start your trading. It is the best site for beginners easy registration and very quickly your account will get activated. Invest small amount and buy only high potential altcoins al the best.