In the lab I am working we culture mESC on MEFs from embryos at blastocyte stage after the removal of the zona pellucida with tyrodes acid.
In this case, you just need to control under a stereoscopic microscope the effect of the acid solution used at RT.
Moreover, if you need you can culture the embryos in KSOM drops at 37º and 5% CO2 up to the desired stage and start then the procedure.
Related to the MEFs we culture it on a NUNC 4-well dish 24 hours previous the culture of mESC in DMEM suplemented with FCS (200.000 cells per well). After the 24 horus culture, we change the medium for the derivation medium containing KSOR and LIF.
To maintain the mESC culture you must change the medium every 48 hours and subculture the stems colonies every 6-7 days post-culture.
For more detailed information you can check this article (http://www.ncbi.nlm.nih.gov/pubmed/20862536) or if you need contact me again!