It is well-known that some ergative languages lack morphological case. If there is no case, where does their ergativity show up?
Abkhaz is ergative and caseless. Verbs have slots that express their arguments by prefixes. An example of an intransitive verbs is с-цоит "I go" (the prefix in the first slot signals the subject's person, gender, and number).
Then there are bipersonal intransitive verbs, such as с-у-суеит "I hit you". The first slot signals the subject and the second slot the indirect object.
Finally, there are transitive verbs. In и-∅-з-боит "I see it" what is expressed in the first slot is the direct object. The subject is expressed in the third slot.
NPs are optionally adjoined to the verb and agree with it in person, gender, and number, thus allowing for free word order.
Circassian, another Northwest Caucasian language, has the same verb structure but since it has morphological case, the verb agrees with its arguments in person, case, gender, and number.
It may show in a number of things.
First of all, in agreement: if the language has bound pronouns, they will differentiate between A vs. S&P (where A is Agent, S is the Single argument of an intransitive and P is Patient).
Another thing is the syntactic ergativity in the wide sense, i.e., any clustering of morphosyntactic characteristics for A vs. S&P. This includes restrictions on relativization, topicalization and wh-movement of the ergative, binding and control priority of the absolutive, coordinate omission (girl-1 kissed-1 boy-2 and smiled-2), and even valency changing derivations (see Letuchiy on Adyghe; it's a language with case, though).
For the work on syntactic ergativity, see Manning's dissertation, Aldridge, and Polinsky, a.o.
Also, in a fixed word order language ergativity could manifest in word order (not that I heard of such, but logically possible).