You will have to learn MIPS assembly, and some information about the processor and the registers it uses (for example, opcodes are 3-operand, and
r0 is always zero).
If you want to add dynamic analysis to your efforts at static disassembly, you'll need the corresponding environment. For example, if your binary is a piece of old SGI IRIX software, a Linux MIPS system won't help you much, since calling conventions, file formats etc. are different. However, this doesn't neccesarily mean you need a MIPS processor, there are various emulators out there for MIPS devices.
Especially in the case of MIPS under Linux, many routers use MIPS processors, and there are several of them that allow you to telnet or ssh in. So, in addition to running an emulator, you could try getting one of those devices, copying your binary there, and running it, possibly under the control of a debugger like gdb or IDA Pro (you need the professional version, the free version and the entry-level version don't support MIPS).