Exchange USD -> Crypto
Firstly, you'll want to move your funds from USD to BTC or ETH as BTC and ETH as are the two most widely accepted forms of Crypto-currency to be exchanged for alt coins on exchanges. I recommend Coinbase as a starter due to their security and insurance of up to $1 Million, similar to how banks have FDIC insurance.
Another option would be Gemini which actually is just as good, as they are founded by the Winklevoss twins, and provide competitive fees.
Once you've attained either Ethereum or Bitcoin, you may now move your money across platforms on the internet. Unlike our traditional payment processing methods of trying to access a broker for trading, you can move your funds to the platform IMMEDIATELY after making an account. Within hours or minutes of making the transfer, your money can be used for trading. However, you will need to upload your documentation to withdraw the funds.
Once you've bought Ethereum or Bitcoin, you're now able to participate in the activities of the wild wild west.
Sign up for Exchanges to trade on
From there, you would then move your coins to an exchange in which alt-coins and other coins are exchanged and traded. "
A few examples of these exchanges would be: Kraken, Poloniex, and Bittrex. These are all available to US Citizens for trading.
Bittrex is my first recommendation as they allow fast executions trading from their web broker. They also have a lot of alt-coin trading pairs, and an active community of users trading many of the coins provided.
Kraken has the advantage of allowing users to short Bitcoin, Ethereum, or Ethereum Classic, however - I've experienced delays in Kraken's execution times at the most valuable moments. I would recommend staying away from Kraken for fast trading.
Wallet to wallet transfer to deposit money onto an exchange
Once you've done this. You can transfer your Bitcoins or Ethereum from Coinbase or Gemini onto the exchanges of your choice. Each exchange has their own benefit. Some exchanges will have altcoins that others don't so you'll want to do some google searching to figure out which exchanges you really need the most.
Here's the important part:
When withdrawing coins from one facility and moving them to another, you are simply withdrawing into a deposit wallet address of the exchange. First, you go to the exchange in which you are moving your Bitcoin or Ethereum into, and you go to funding. From here, they'll give you deposit addresses for each type of Crypto. Take your address and put it into the Address field on the Withdrawal page for Coinbase or wherever you are currently holding your coins. Once you've confirmed the amount and clicked send. (NEVER HAND-TYPE AN ADDRESS, if the address is wrong the funds are gone) The funds should be moved within 15 minutes. You can confirm transactions on etherscan.io and blockchain.info for Ethereum and Bitcoin respectively.
Trade Between USDT, BTC, ETH
Some brokers offer the use of "tether" for tax purposes. Tether holds the same value as the USD dollar so it makes for a great replacement on Bittrex. You can also trade many alt coins with ETH or BTC, in fact, most of the good alt coins require BTC to be traded on Bittrex.