According to NASA, causes of the Earth's greenhouse effect include water vapor, carbon dioxide, methane, nitrous oxide, and CFCs.  Carbon dioxide gets the most press, and NASA's page says:

Carbon dioxide (CO2). A minor but very important component of the atmosphere, carbon dioxide is released through natural processes such as respiration and volcano eruptions and through human activities such as deforestation, land use changes, and burning fossil fuels. Humans have increased atmospheric CO2 concentration by a third since the Industrial Revolution began. This is the most important long-lived "forcing" of climate change.

An article by NC State University says that a healthy tree can store 13 pounds of carbon per year.  As I understand it, carbon dioxide is processed by the tree: the carbon is stored, and the oxygen released.
Given that, how many trees would I need to plant to solve the global climate change crisis?  Should I optimize for a specific type of tree, or would pine work as well as oak or black walnut?

In 2010 anthropogenic emissions (not including land use change) were approximately 9167 million metric tonnes.  Your data on trees holding 13 lbs (5.9 kg) of carbon per year equates to 169.6 trees per metric tonne of emissions.  

So to take up all of the emissions from 2010 you would need 1,545,000,000,000 trees.  A mature forest has only about 100 trees per acre (400 per hectare), so you would need 15,545,000,000 acres of mature forest.  This equals an area of 24,290,000 mi2 (62,910,000 km2).  This is approximately the land area of Asia, Europe, and Australia combined!
The surface area of land on the planet is about 150,000,000 km2, so in principle we would need to add cover onto 42% of the current land (or we could take soil from deep ocean floors to landfill 1/5th of the oceans!) in order to plant enough trees to solve the problem.

This also assumes that the 13 pounds (5.9 kg) of carbon figure is for mature forests, rather than for growing trees (see comments for further discussion).  If this value is for young developing trees, it would indicate less be attainable in the longrun.  If the 13 pounds is for a developed forest, perhaps a greater amount could be removed in early years as a temporary quicker fix.

There is also the problem that forested land is likely to have a lower albedo than the land surface that it covers, and hence the planet will reflect less sunlight back into space which would lead to some extra warming, so we would also need to compensate for that somehow.  Apparently about 26% of Earth's land is already covered with forests.  I rather doubt over half of the uncovered land surface is suitable for new forests, the continents have large bands either side of the equator that are generally too arid, and the regions close to the poles are too cold.

In short, it isn't going to work, even with the most generous assumptions about forest CO2 exchanges (unless of course I have made an arithmetic error, which is definitely a possibility).
