The full, "proper" catechumate rite, involves renouncing sin and (if applicable) the key errors of one's past religious affiliation, and then the profession of the Orthodox faith as well as the promise of obeying the lawful Orthodox hierarchy and pastors. As part of the renunciations, one does "spit" at the devil, but one should keep the saliva to a bare minimum.
In some places, this full rite is kept until the last minute, until the time of Baptism (or Chrismation where applicable). Hopefully, the renunciations are being observed whatever the case, since their ommission is incorrect and extremely "telling" in it's own way (and if not so, then just incredibly negligent.)
We're very fortunate in our parish, as the Priest makes a point of having this little ceremony (in full) at the begining of everyone's catechumate (thus making it official and not informal), and has it right after the Divine Liturgy on Sunday (so as to have everyone present in the parish, to be witnesses.) It's a nice, and fairly brief ceremony.