I have an excel table with mobility data from a few households....the columns are something along the lines of PersonID, HomeAddress, PurposeOfWay, WayNumber, StartTime, EndTime, DestinationAddress... Each person has a few ways associated with them. I would like to display this data somehow but I'm stuck. 1. person - 1. way - 2. way / 2. person - 1. way - 2. way - 3. way... and so on. I'm not sure how I should go about it? I used ArcGIS to geocode the home addresses...but what now? Maybe someone has already done something similar and can point me in a direction?
This is a pretty broad question with a lot of sub-components that have been answered at other questions here. It might get flagged as too broad, but I'll try to give you some direction so you can either edit or come back with more specific questions.
You want to show lines on a map that represent Ways and symbolize them by person (or purpose, or number, or whatever). You're going to need a few layers to do this, starting with a point layer of home addresses (sounds like you have) and a point layer of destination addresses.
Then you're going to need a line layer for the routes. The lines could be created yourself by digitizing, or if you have access to Network Analyst there are a couple of approaches you could take to automatically generate the lines for you. You'll need some sort of base layer of streets to follow - if digitizing yourself an ArcGIS basemap of streets would suffice, but using Network Analyst would require some line streets data (for instance TIGER data) that could be built into a network. The digitizing yourself approach will be simplest but most time consuming. The Network Analyst approach will take more up front learning but be quicker to acutally solve/generate your lines.
The second major issue you'll face is joining your table data to your line data. If each line is a unique route, and each record in the table is a unique route/person combination, your lines would need an attribute that could match up to that combination in the table. For example, a new field in the table that combines person and route as 1-3 or 2-5. Then an attribute in the line data with that same 1-3 or 2-5 value. With that present you can do a join/export to transfer the route information to the lines.