There are many ways to investigate apoptosis in vitro.
As mentionned above, you could use any of these kits for Annexin V-PI staining. This will quantify phosphatidylserine translocation to the outer layer of cell membrane (an early marker of apoptosis).
You could also use a caspase3/7 activity probe from invitrogen. Its considered as an early marker too.
You could do cell cycle analysis by flow cytometer with PI/RNase solution to quantify DNA fragmentation. You coukd obersve DNA fragmentation by agarose gel. And finally, you could blot markers from the apoptotic pathway by Western Blot!
For flow cytometry, I use preincubation with CaCl2 2.1 mM + Alexa647 Annexin V from Biolegend.
Kits usually have the concentration of CaCl2 2.5 mM, but I haven't seen much of a difference between 2.5 and 2.1, but with 2.1 mM you have a lesser chance of additional cell activation.