A DApp consists of two parts:
The Ethereum contract
The Ethereum contract is executed by all the nodes in the network. All you need to do is deploy the contract, and it will be executed by all the nodes forever. You can deploy a contract from most Ethereum client programs. You don't need to do anything to keep it online. Ethereum contracts are usually written in the Solidity programming language.
The user interface
You do not have to create your own currency to create or to use a DApp.
To use a DApp, the user needs to install an Ethereum node or a browser plugin on their computer. For example:
- MetaMask (browser plugin)
- Parity (PC program & browser plugin)
- Mist (PC program with built-in DApp browser)
There are no 'Ethereum servers', there are only Ethereum nodes. These nodes run Ethereum contracts.
You are responsible for distributing the user interface, usually by hosting it on a website, but you don't need to do anything to keep the Ethereum contract running.