Plural verb: How are things going? :tick:
Subject-Verb agreement: Things are going well. :tick:
Contraction: How're things going? :tick:
Singular verb: How is things going? :cross:
Subject-Verb agreement: Things is going well. :cross:
Contraction: How's things going? :tick: (spoken English)
Note, when you contract how is to how's, the verb gets lost in the phonetics, so, no verb, no agreement--at least at the phonetic level. ;-)