Almost every wallet on in the app store has the ability to exchange coins via an external exchange and some can even exchange them through a decentralized exchange (DEX). If you live in the US, Coinbase is a good option although it is more of a bank than a wallet as they hold the private key to your wallet and can close your account at any time.
On exchanges you can link your bank or send wire transfers to the exchange and then exchange your fiat currency for any altcoin of your choosing. Exchanges like BitTrex and Poloniex that service the US have MANY more altcoins pairs listed than the wallet options.
You can convert one coin to another using Changelly. If you want to convert your own coins or the person or entity you are transacting with requests or requires another coin, you can make that happen for most of the major coins. You only need the sending and receiving addresses.
The basis of human civilization, in real life, face to face agreements made between two consenting parties to trade an amount of one coin, for an agreed upon amount of another coin. There are some cities that host open air exchanges where you can swap coins in person.
Another method of converting USD to BTC is getting your payroll checks directly deposited to Bitwage where they convert it to BTC. You can optionally have the BTC automatically forwarded to another address. Here is a video on how to get setup with Bitwage. The difficulty is the tax implications every time you cash out your crypto to fiat so you can pay bills at which time you create a taxable event.
There are quite a few sites for online work as a freelancer that pay in cryptocurrency. You may also be able to work out a deal with your employer (especially those in the tech sector) to be paid fully in crypto. The difficulty is the tax implications every time you cash out your crypto to fiat so you can pay bills at which time you create a taxable event.
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I am not a financial advisor or tax professional. You should always consult with a licensed professional when regarding your financial investments and tax situations. Do your own research into all aspects of your investments and do not invest in something you do not understand. Remember, never invest more than you can afford to lose!