There are two stages to what you want here.
1. Converting point data to gridded data
First off, since you want to plot regular cells rather than the actual data that you have, you need to covert your point data to cells in some way. The best way to do this may depend on the data itself, but one way would be to interpolate, perhaps using something along the lines of,
SI = scatteredInterpolant(Lon, Lat, Rain, 'natural', 'linear')
% read up on and understand the last two parameters before choosing what to use
%form the grid, with points 1 degree apart.
gx = min(Lon):1:max(Lon);
gy = min(Lat):1:max(Lat);
[ X, Y ] = meshgrid(gx, gy);
%produce an actual grid of rain data
gridded = SI(X,Y);
Alternatively, if your point data has a much higher resolution than the 1 degree grid, and if it is regularly spaced, you could simply take the mean of the points that lie in each cell.
2. Plotting that grid
A naive method, which might be helpful as a quick check that what comes before has worked, would be,
However, that will treat lon and lat as x and y coordinates on a rectilinear grid. To plot with a projection (N.B., WGS84 is not a projection. You'll need to figure out exactly what you're after with more clarity), you ideally want the Mapping Toolbox. I'm not an expert on that, but it should make projected plots relatively straightfoward.
If you don't have access to the Mapping Toolbox, then you could spend a lot of time faffing with coordinate transforms to do what you want... but my advice would be to spend the time learning the basics of a GIS package instead (QGIS is free) and use that to do the job.