Most often, such a thing would be demonstrated by a witness, often the plaintiff, simply testifying, describing the events. A video or pictures, identified by testimony, might help the events to be more vivid to a court. Corroborating testimony by an additional witness might also be of value.
But I suspect the major question here will not be the evidential one of "Did these events happen", but the legal question of "Did these events violate legal rights?"
Recall that "use and quiet enjoyment" is something that the landlord contracts to provide to the tenant, not a general right as against the world at large. If the landlord has failed to take sufficient steps to provide "quiet enjoyment", a tenant might have grounds of action against the landlord. Any direct action against the other tenant's guest would have to be by means of some general law, much the same as a householder taking action against a passing stranger. That would sepend on the local law, which would depend on the (unbstated) jurisdiction.
What constitutes interference with quiet enjoyment and what actions can be taken to remedy this also depends very much on the local laws. No more detailed answer can be given without knowing what country this is taking place in, and if a Federal country such as the US or Canada, what state or province. Moreover, landlord/tenant law is often truly local law, and may be different in different cities or counties. A specific location may matter.