I'm learning how to use Network Analyst, and I'm not entirely sure what to do (or search for). My objective is to measure the nearest distance from the red circles to the blue circles along a road network:

I have made a network in ArcCatalog using the network wizard and I'm just interested in the simplest network distance. My network looks like this:

Is this calculation possible to do? My red points are generated as centerpoints of a grid as I am just interested in the average distance for each grid. I realize that these red points are not on the network, so I'm not sure if that is a problem for the calculation.
What should be my next steps? (after reading more of the help documentation!)

