Choosing solar panel - how many watts?
Typically a smartphone will need around 1A, the newer fast charging cell phones need 2A. 1A should be find in phone charging application. USB runs at 5V so on the low end 5W on the high end 10W (1A*5V is 5W)

A good low number for a sunny day is 400w/m^2 (up to ~1000w/m^2 dependent on latitude, angle, and conditions), multiply this number by the panel size. If a panel is 0.04m^2 10W of solar energy on the face of the panel.

The panel can't convert all of the energy to electricity, so multiply the last number by the panel efficiency (if they don't have it listed, don't buy it). A typical number is 12% so you'd get roughly 1.2W out of a 0.04m^2 panel. 

Which would only be 1.2W/5V = 0.24A, which would still charge the cell phone, but at a much slower rate. The solar charge controller will also take this number down as at most they are ~90% efficient.

That means a larger panel would be needed in this case, or two of them. Remember you need a solar charge controller with MPPT capability to convert the power at the highest efficiency.