The President said "We're getting out. But we will start to negotiate, and we will see if we can make a deal that's fair."
According to the Paris Accord itself the agreement doesn't require any specific level of emissions cuts. Each nation, including the US, gets to choose its own level of emissions reductions and decide what's fair.
The President could have just changed US emissions targets and stayed in the deal. So that statement is MISLEADING.
According to the Washington Post, the U.S. does contribute to something called the "Green Climate Fund," as President Trump noted in his speech. That’s a pool of money that pays for climate change improvements in poor nations.
In his speech, the President claimed those funds were being "raided out of America's budget for the war against terrorism."
But the Post reports US contributions to that fund come from the treasury, and not some war chest to fight terror. So that claim would be FALSE.
President Trump also said “even if the Paris Agreement were implemented in full...it is estimated it would only produce a two-tenths of one degree...Celsius reduction in global temperature by the year 2100."
It is true that current commitments from the nations in the Paris Accord are not enough to meet the two degree reduction goal set by the agreement.
But this analysis by MIT found it would reduce the planets warming a full degree celsius in that time. A cut that would have a positive impact on the environment according to scientists.
So that statement would be FALSE.
Finally on China, the President said "China will be able to increase these emissions by a staggering number of years -- 13. They can do whatever they want for 13 years. Not us."
Again, the agreement does not bind any nation to any emissions target. Each nation can set whatever goals it chooses.
The Washington Post reported it is true that China chose to let it's carbon emissions continue to rise for the next 13 years before then declining.
But that same reports says to ensure that happens, China cannot do "whatever it wants" as the President indicated. And in January China actually cancelled plans to build more than 100 coal fired power plants.
So that statement, is MISLEADING at best.