How Bitcoin wallet works is pretty simple. Bitcoin works by transferring tokens in between wallet addresses, which can be created at will. Bitcoin never actually leaves the blockchain, instead, its position on the blockchain is updated when a person chooses to send the token to another wallet. The user has a private key, which is what the wallet stores.
In the beginning, Bitcoin wallets weren't especially user friendly. This has changed, and today you can download a hot wallet that will work on your smartphone or PC for free. With this wallet, you can input addresses for the Bitcoin blockchain and many others, and transfer tokens.
The Bitcoin wallet manufacturers go out of their way to make the products as easy to use as possible, and many feel like a banking app. You can choose whatever fiat currency you wish your token balances to be displayed in, and you can also use this as a way to send a fixed amount of Bitcoin, or any other token the wallet supports.
If you want more security, it would be a good idea to pick up a cold wallet, which is a hardware device that does the same thing as a hot wallet, but isn't connected to the internet.