Step one: firmly restrict the debate to gun CRIME. Suicides are a different dynamic and do not belong in the battle of the body counts. Get your opponent to draft the definition FIRST, so he or she cannot credibly back away from it.
Consult the FBI's "Crime in the USA", aka the "Uniform Crime Reports" (not really the name, IIRC, and it might not be called CITUSA any more either).
AND get the predecessor data for NYC back to 1900. "Sullivan Law" in 1911, IIRC, made it almost impossible for peasants to buy or own handguns without following strict licensing protocols. Greater and greater restrictions on rifles followed over successive decades.
Trend lines.
Add to trend lines "major" pieces of legislation, such as GCA '68 (national), which did away with "mail order guns", federalized through the Commerce Clause and the FFL system and imposed a 21-YO minimum to buy an evil handgun, but kept the "adult" definition of 18-YO to buy a long-arm from an FFL. Technically applies to guns that have traveled in interstate commerce, and in most states has had a private party "loophole" of local law rules.
Try Washington, DC, "freezing" existing handguns in 1976 (a great bicentennial gesture, eh?) and requiring all existing ones kept in homes to be disassembled. "Model" gun control laws per the gun-grabbers. "Murder Capital" of the nation through most of the '80s and '90s and still is no slouch on the body count to this day.
Pinpoint years that each successively stricter handgun law was enacted in Chicago/Cook County/Illinois (the latest under Barack Obama's watch). Show where the trendline goes after each law.
Pinpoint "Operation Exile" in Virginia, one of the so-called source states for DC's "illegal" handgun supply. By targeting existing "prohibited persons" who had already been committing petty crimes, the victimization of the law-abiding by them dropped. No new laws, just FEDERAL initiative to enforce Federal laws that some of us consider marginally stupid. However, incarceration worked by incapacitating the minor violent people before they killed or injured us, and keeping those who had killed or robbed already out of circulation during whatever sentences they got.
Nationally, pinpoint the sudden wide availability of standard-capacity handgun magazines for non-LEOs beginning September 13 four years ago and how much crime "jumped" in the years since.
When your liberal mush-head blames the violent-culture carnage of our biggest cities and their strict laws on neighboring states with "weak" laws, point to Jamaica as an example of the national approach. They banned handguns AND ammo in 1976, set up special gun courts with severely restricted civil rights and liberties, and they had successes in reducing gun murder, gun robbery, and gun trafficking rivaled only by the crime-reduction successes of Detroit. It's so bad now, the UN is looking at some special initiatives to reduce crime there, which focus as much on social factors as on their pie-in-the-sky efforts to reduce the "illicit trade of small arms". Clue--the illicit trade is fed by a violent, scofflaw culture that does not value life like most of in the US do.
There may even be some study somewhere that showed the total number of handguns in Windsor, Ontario across the bridge from Detroit is similar to the number of handguns legally in Detroit... Number of crimes committed per gun in Windsor is a lot smaller than the number of crimes committed per gun in Detroit.
But be warned: I have encountered few starry-eyed liberals who were willing to let facts get in the way of their pipe dreams. Remember, these are often (not always) the same bunch of doughheads who cannot see the similarities between white supremacist groups and Muslim supremacist groups. Sadly, they cannot/will not see the differences between the skinhead hate groups and the raghead hate groups, either--and the resist recognizing the similarities and differences far more stubbornly than any anti-Arab bigot I've ever encountered, BTW.
Finally, look into the TOTAL murder rates, and robbery and all violent crime for Japanese-culture US citizens, and compare them with TOTAL murder rate, robbery rate, and violent crime rate in Japan. Japan has been largely disarmed of effective personal weapons (starting with its racist oppression of Okinawa and spreading into their own land) for more than five centuries. Fewer guns there than in Canada.
You will find that crime is fed by:
1. Cultural and societal factors first.
2. The percentage of overall population which consists of males age 16-26.
3. Unreliably, education and economic opportunity
4. MORE reliably, city size and population density (there was a great stats study of California in the Rifleman maybe 10 years ago)
5. and LEAST reliably, the "availability and access to" weapons.
Then look at England and Australia and you will find that their own measurements of overall crime were helped the first 1-3 years after each oppressive gun law, then resumed their steady climbs, fed by the first 4 factors listed above.
Suggested approach to "cherry-pick" the cities to look at: identify the states and cities which get the "best" gun law ratings from the Brady Bunch. Hit that hard.
Be prepared to be baffled by your opponent giving up the debate and returning to fluff which questions anyone's "reasons" to own killing devices, and which revolves around the ideas "should" and "should not".
Then show that film clip of John Wayne's sheriff character in True Grit grousing about certain people who "need killing", and use all that "should" logic with "pro-choice" logic to just close with the idea that some of us understand that some evils in the world cannot be solved with community group counseling, and we claim the human right of self-preservation, especially when the rule-breakers attempt to harm us or other innocents--because when the bad people need killing, it's more fair and sensible to have them shot before they can harm the innocent, rather than shot by cops as they are fleeing the bloody crime scene. GET THE CONCESSION THAT NOT EVERY "GUN DEATH" IS A BAD THING. ESCHEW THE "VIOLENCE IS NEVER A SOLUTION FALLACY.
Finally, quote all the hysterics of "old west" style shootings that were going to make blood "run in the streets" of Florida when it started the trend of "shall-issue" CCW. THEN point to Florida's spike in crime perpetrated against tourists driving rental cars, because the gang-bangers KNEW their victims were not locals and could NOT CCW.
Announce your conclusions about your opponent's intelligence only after all this is done. Plan for 90 frustrating minutes.