Edge rate control is done with either drive-strength limiting in the source or series resistors close to the source. For example, sticking 100R resistors on all of your serial clock and data lines close to the source (eg: clock, CS, MOSI for a SPI master, MISO for a spi slave) is usually a decent start.
Yes he means a solid ground plane, so the return current for any of your relatively high speed lines is free to travel on the ground plane directly beneath the trace, rather than having to detour around because of an obstruction, increasing the inductance and EMI.
Remember that current flows in a loop. If device A drives a line high, the current will flow out of device A, into device B where it's attached, through device B's internal circuitry, out device B's ground pin, through the PCB ground plane, back to device A's ground pin. For very low frequencies, the term "current follows the path of least resistance" is true. This ground return current will bias toward whatever path gives it the least resistance, usually a straight shot between the two devices. As the frequency increases, this starts to break down. The truth is that the current doesn't follow the path of least resistance, it follows the path of least impedance. For DC, impedance is just resistance, but when the frequency increases, reactance starts to play a part as well. When you get into double digit MHz, the impedance will be heavily affected by reactance, which means the return current won't just follow a straight shot from device B back to device A anymore, it will follow whatever path minimizes reactance. Any loop created by the source current and return current paths is an inductor. To minimize loop area and inductance, the return current will tend to follow a path directly underneath the trace. It's important you allow this to happen by having a solid, obstruction-free ground plane. Don't run any other traces on this ground plane if you can help it, and certainly don't run any traces directly under your high speed lines or you'll obstruct the return current for those lines.