I've taken a GIS course where we would complete projects based on data sets that were provided for us.
I'm in a position where I need to create my own data set in order to begin analysis.
Any help regarding how to go about doing so would be appreciated.
You could start to download the spatial dataset from the Government's Open data website where suits your area of interest.
E.g. cadastral data from local government, demographic data from National Bureau statistic, satellite images from USGS, Geoscience Australia, etc. to build your own dataset that relevant to your topic.
Below is the analytics tool link for tool usage.
Become familiar with the help files. They are excellent
Progress to courses (which are available) once you are familiar with terminology and process.
Good places to start
include all the sublinks, the above are just the main starting points.
Other main links are within the main help page
As for creating data to analyse... think of something as well that might be of interest, so you aren't mindlessly doing a poke and click pre-packaged plan of which you have no interest.
There have been some good suggestions from @VickyWang and @DanPatterson. However, it really depends on what type of data you are using and for what purpose. A simple example is if you are using point data in an analysis. You could create a csv or excel file, containing latitude and longitude of the points, along with other information, and just import it into arcGIS.