What should I consider when converting a double-basin sink to a single-basin?
Remove everything currently under the sink that is not glued and use a rags to plug the drain pipes.  Next, let the counter guys do there work and install the sink.  There is nothing to do until they are done.

After they are done, follow the install instructions on the disposal.  After that is done, mount a new p-trap kit from one of the drain pipes to the disposal outlet.  Choose which one works best.  The other drain pipe you will need to cap.  Since this is under a sink, you can use a compression based cap so if in the future you decide to go back to a two sink setup it will be an easy job to removing the cap.

There is no harm in trying and if you find it doesn't work/leak just call a plumber.  The plumber I use, this would just be a service call charge ($45) to install.

Also if you plan to reuse your current disposal, remove it and the mounting ring before the counter guys come.  I had a friend who had they counter/sink redone and the counter guys left with the disposal mounting ring still attached to the old sink.  They had to buy new hardware to mount their old disposal.