A "mi sheberach" is a public prayer or blessing for an individual or group, most often recited in synagogue when the Torah is being read.  There are mi sheberachs for just about any person in need of some divine goodness in a synagogue its most notably for those requiring healing.
When we petition G d to bring blessing or healing, it is customary to do so in merit of charity pledged. So if you request that a mi sheberach be said in your synagogue on someone’s behalf, make sure to give some charity as well (of course not on Shabbat).
The prayer is recited by mentioning the individuals name and mother's name - preferably the Jewish name.