A doge miner is hardware that uses its processing power to mine Dogecoins by helping complete people's transactions. When a transaction is completed, a number of Dogecoins are created and divided amongst the miners that helped with the transaction. Miners fall into 4 categories, CPU, GPU, FPGA, and ASIC.
Stands for: Central Processing Unit
CPUs are the most basic (and usually weakest) type of mining hardware, and every computer has one, making them easy to attain. CPUs usually have a hashrate of <10 MH/s, (Megahash per second) and mining solo with a CPU will not usually offer much benefit.
Stands for: Graphics Processing Unit
GPUs are one step up from CPUs and will usually offer a hashrate from 10 MH/s to 1GH/s and they have fairly high availability. Their purpose is usually to do the heavy lifting for complex graphics, and that's the same type of math that it takes to mine Dogecoins. They are one of the most common forms of Dogecoin mining. Solo mining is possible with a GPU, but when not carrying an exceptionally powerful GPU, pool mining is usually the best course.
Stands for: Field-Programmable Gate Array
FPGAs are usually more powerful than GPUs, but not always. They usually produce from 100MH/s to 10GH/s, and are less commonly used than GPUs. Solo mining is usually easy with FPGAs.
Stands for: Application-Specific Integrated Circuit
ASICs are much more powerful than all other mining forms on this page, much more powerful, with a hashrate range from 1GH/s to 10 TH/s. Some types are more common than FPGAs, but ASICs are fairly rare. Solo mining is very easy with ASIC miners.