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Create an Account on an Exchange
Like other cryptocurrencies, Ethereum must be purchased and sold via an exchange online. There are a number of these services that are available and are considered highly reputable. Some of the most popular include Coinbase, Kraken, Bitstamp, and Gemini. Before you can get started trading Ethereum, you'll need to pick an exchange and create an account.Verify the Account
Any reputable exchange will require that you verify your account in one or more ways. You'll likely need to upload a number of documents to verify your identity and ensure that your account passes regulatory muster. Verification will typically take a day or two, depending on how popular and busy the exchange you've selected is.Deposit Fiat Currency
You'll next need to deposit fiat currency into your account, typically via bank or wire transfer. This may take another few days in order to ensure that the money clears.Begin Trading
With a verified account and money deposited into that account, you'll be able to begin purchasing Ethereum and other cryptocurrencies via the exchange. Each exchange has an interface that works somewhat differently, but be prepared to confirm transactions and then allow for processing time, which can also depend on the total number of transactions requested.Withdraw ETH Into a Wallet
Once you have purchased ETH through the exchange, you can then withdraw that currency into a wallet that you control. Exchanges can be hacked, meaning your tokens can be stolen. In order to keep your tokens in a private place which you have access to via key, download and install a wallet which has Ethereum capabilities. Run and set up the wallet, creating a new account.
You can then input your account address into the exchange in order to transfer your ether to your wallet. Be sure not to use your wallet address, password, and private key, or else you may have trouble accessing your ether later on. Transfer it back to the exchange to sell or continue trading at a later time.