The first place to look for a weakness in your opponent's motion is at their legal argument. Assuming the evidence is what they say it is, is the legal argument correct? Shepardize their cases. Are they still good law? Is there a case squarely in opposition to the cases they cite? Is there a case with the opposite holding from a higher court? If the legal argument is incorrect, bring that to the court's attention as your first order of business.
Attack the Evidence
Examine your opponent's evidence. Do the declarations have an adequate foundation? Do all declarants have a basis of knowledge to declare the things they are declaring? Do the declarations contain hearsay? If so, are there any applicable exceptions? Is the deposition testimony based on an adequate foundation? Chances are your opponent is offering evidence with at least one major admissibility problem. Make sure that you include a separate pleading setting forth objections to your opponent's evidence. But beware: do not shotgun objections to all of your opponent's evidence. Rather, select the one critical flaw with the one dispositive piece of evidence and bring it to the judge's attention. Note that all objections are waived unless made on the record. Be persistent with your objections, and insist on rulings at the hearing. That way, you are sure to preserve your record for an appeal if your opponent prevails at the trial court level.
Attack the Separate Statement
Focus on your opponent's separate statement of undisputed facts. Find the one fact that if disputed with competent admissible evidence would defeat the motion. Then, offer evidence to dispute the fact. Make sure to focus the court on the key dispute in the record, and be sure that your evidence is admissible, and that the fact in dispute is material, not trivial. In other words, it should be a fact that if found your way by a jury, it would turn the case.
Consider Whether Your Opponent's Motion Meets its Burden
Under Schieding v. Dinwiddie Construction Company (1999) 69 Cal.App.4th 64, you need not submit any evidence in opposition to a motion for summary judgment if the motion fails to meet its burden in the first instance. Apply a demurrer standard and ask, if accepted, whether the motion standing unopposed would be granted. If the answer is "no," then make the first part of your argument that you really need not submit any evidence in opposition, and that the motion should be denied out of hand. Your second argument should be that in any event, your evidence creates a triable issue.
Consider Seeking a Continuance to Conduct More Discovery
All oppositions to summary judgment motions should end with a request for a continuance of the hearing to conduct further discovery. Not only should you request a continuance, but you should include an example of the actual discovery you would conduct if given more time, an explanation of how the evidence you expect to discover would defeat the motion, and a good reason for why the discovery has not yet been completed.
I highly recommend that you read Thompson/West's Civil Procedure Before Trial on summary judgment, and pay special attention to the section on ruling on the motion. Focus your arguments on the burdens of the parties, and always argue that your opponent failed to meet the burden. Think like a judge ruling on the motion, argue reasonably, never misstate fact or law, and be humble and polite at the hearing. Good luck!