Short answer. The plaintiff goes first on the complaint, then the defendant presents evidence on defense, counterclaim, cross-claim, and third-party complaint, then any third-party defendant, then any fourth-party and so on, then parties facing a counterclaim or cross-claim defend against it, and finally all parties may offer only rebuttal evidence, unless the court permits more.
What the law says
Subject to the provisions of [S]ection 2 of Rule 31, and unless the court for special reasons otherwise directs, the trial shall be limited to the issues stated in the pre-trial order and shall proceed as follows: (a) The plaintiff shall adduce evidence in support of his or her complaint; (b) The defendant shall then adduce evidence in support of his or her defense, counterclaim, cross-claim and third-party complaint
Rule 30, Section 5 — Order of trial. Read the full provision →
The step-by-step sequence
The order runs: plaintiff's evidence on the complaint; then defendant's evidence on defense, counterclaim, cross-claim, and third-party complaint; then any third-party defendant's evidence; then any fourth-party (and further) evidence, following the same pattern down the chain of parties; then evidence from parties defending against a counterclaim or cross-claim brought against them; and finally rebuttal evidence only, unless the court permits the introduction of further evidence for good reasons shown.
Trial is confined to the pre-trial order's issues
Subject to Rule 31, Section 2 on separate trials, and absent special reasons the court identifies for departing from the usual sequence, the trial is limited to the issues stated in the pre-trial order — not the pleadings generally, which may have raised more or different issues earlier in the case. The order of proof exists to methodically walk through exactly those defined issues, one stage at a time, rather than allowing the parties to range freely over whatever the pleadings once alleged.
Multiple defendants with separate counsel
Where several defendants, or several third-party defendants, appear with separate defenses through different counsel, the basic sequence set out above doesn't resolve conflicts among them on its own. In that situation, the court determines the relative order in which their respective evidence is presented, since the rule's default sequence assumes a more straightforward alignment of parties on each side than a multi-party case with divergent defenses actually presents.
What happens once evidence is admitted
Once the evidence from all sides has been admitted, the case is deemed submitted for decision, unless the court directs the parties to argue orally or to submit memoranda or any further pleadings before deciding. That submission marks the formal close of the evidence-taking phase of trial, after which the matter moves into the court's deliberation on the merits, subject only to whatever further oral argument or written submissions the court has specifically called for.