r - Checking if Lng and Lat fall inside polygons from ESRI Shapefile

I have two input files.

First: CSV file with a list of points each defined with Lng, Lat, Name

Second: ESRI Shapefile defining a number of polygons

I would like to determine for each point I have (from the CSV file) which polygon does it fall inside (if any)?

I will be using R.

I know that this might be a straightforward task but I am totally a newbie to GIS.

I have done some searching, and I have found that I can use "MapTools" package in R to load the ESRI shapefile, but I don't know how to move after that.

I managed to read the shapefile using readShapePoly function in the MapTools package and now I can plot the polygons and iterate through them in R. I also loaded the points from the CSV file into a data frame with two columns (lng, lat). Now I need to check for each point which polygon does it fall inside (if any)...

I managed to do this using the function over from package sp in the way explained here, however I am getting NA result for all points which is unexpected. I think it is due to different projections for the points and polygons.. Examining the polygons loaded from the shapefile using summary function gives me Is projected: NA, proj4string : [NA]

Any tips ?

Any advice, good tutorial or code sample showing how to do that would be highly appreciated.