I need to be able to set up a soil sampling grid at regular spacings of around 50 - 100 meters. Then export the points to a GPS so I can be guided to the points. I am new to GIS and have tried to do this with QGIS and ArcMap 10 - so far with no luck.
The "Regular points" tool should do what you need:
Note: The project should be set to a coordinate system with unit meters (instead of degrees).
To further adjust the grid, you can use "Affine Transformation" tool to rotate and move all grid points.
Depending on the complexity of your field boundary, the fastest solution for deletion of points might be to simply do it manually.
One question is whether it is necessary at all to play around to fit the grid to the field. Do you have a way to measure goodness-of-fit? Or are you just looking for something that looks nice?
Althoug the answer of underdark is definitely faster here, a general approach that would work with any GIS program is to generate a table with all your x and y values. This is something you can do in excel or in a database (in a database you can use a cartesian product: cross join). Then save your file as .dbf or .csv. Most GIS programs can read those files and convert your coordinates to points.