Which geoprocessing tool or what process are you trying to use? Many of the tools in ArcMap/Catalog are geoprocessing tools.
[ESRI software] An ArcGIS tool that can create or modify spatial data, including analysis functions (overlay, buffer, slope), data management functions (add field, copy, rename), or data conversion functions.
Is there a tool you have seen that is not a standard tool? You can use programming languages like Python to write custom tools (or combination of tools) and then if your have ArcGIS Server, you can even publish some.
Python is the included programming language that can be used (arcpy) to perform many tasks, either as scripts, or interactively using the Python tab (find this under the Geoprocessing tab in ArcMap/Catalog) and Model Builder can also be found there. Model Builder is a graphic way to put together your geoprocessing workflow so may be easier when first starting out (if you are not already familiar with Python).
Please provide a little more explanation of what you are needing.