For a small amount between $10-$250:
You can use many fiat on-ramp serves directly in AlphaWallet browser. For example, you can use Wyre and MoonPay by opening below URLs in AlphaWallet browser: pay.sendwyre.com or buy.moonpay.io or instant.ramp.network/
Tips: For Android users, you can go to Browser -> Get Crypto and see more apps which buy/see crypto with fiat.
For a middle size amount between $250-$50K:
You can use regulated stablecoin services in the AlphaWallet browser. For example, you can use USDC and PAX by opening the URLs below inside the AlphaWallet browser: usdc.circle.com/start or account.paxos.com/login
Compare the USDC/ETH, PAX/ETH, BUSD/ETH rate on 1inch.exchange.
For example, if I want to buy 10,000 USD, I found that the USDC/ETH rate is the best available.
Open usdc.circle.com/start in AlphaWallet Browser, follow the instructions to set up your circle account and start minting the digital dollar stablecoin USDC.
Once you have received USDC in AlphaWallet, open 1inch.exchange to swap the USDC into ETH (UNLOCK then SWAP NOW).
Rate comparison, 1inch vs MoonPay vs Binance:
Once you have the USDC in AlphaWallet you can use any of the other DEXs on Ethereum, such as UniSwap and SushiSwap.
For a large size amount over $50K:
Break your trade up into smaller trades using the above method or find a profession OTC service whereby you can negotiate a good fixed rate.