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Microprobing involves using a micro-positioner with a precision needle under a microscope to to either measure or induce voltages onto an IC. This is very similar to how you might use a multimeter on a circuit board but at a much smaller scale.
A probing station is essential for live analysis. The quality (tip size, stiffness, etc) varies considerably within and across manufacturers. Want to send me your equipment for an evaluation? I'll be more than happy to get some samples ;) This page is mostly focused on mechanical probing stations. Probing cards also might be useful, need to look into them.
mcmaster general recommendations:
Seem to be mostly intended for cryogenics, but might also be suitable for room temperature work.
Seems to be a popular manufacturer. Their equipment can be readily found on the surplus market. Quality varies from model to model.
http://www.quater-research.com/
http://www.miller-design.com/micropositioners.htm
Relatively low price
Use long working distance objectives
Mitutoyo M Plan Apo are pretty industry standard. Consider using SL for 50x and 100x. I've heard that enpdv objectives are a decent quality low cost alternative, but I've never used them
A good lower price option are B&L Industrial objectives. These are finite objectives and seem to be dominant in that era of microscope equipment.