friedo pretty much nailed it all.
Just a little extra info on the monitoring aspect: Often, you can also connect your inverter or system to the internet for a real-time view of generation data. Here’s an example of a random household system that uses Enphase microinverters in London, ON: The SOLAR Store
You can see how much power it’s generating at the moment and how much it’s produced in the past few hours/days/months on a nice graphical interface. There are smartphone apps too.
Vendors other than Enphase also have similar systems, and you can upload your data for public comparison / competitions on sites like PVOutput.org:
Latest Outputs
And at the bare minimum, as freido said, usually the inverters will have some sort of display built in to it, or at least some sort of port you can plug a computer into, to monitor what it’s doing.
If you get a good installer out there, yeah, they should be able to give you a reasonably good estimate. If you want to do it yourself, you can start with something like the PVWatts Calculator:
http://pvwatts.nrel.gov/ (run by a US government agency in conjunction with a renewable energy lab)
The one thing that’s not great at estimating is how shading will affect your location. For that, you can use something like a solar pathfinder (Solar Pathfinder - Solar Pathfinder), basically a big fisheye lens overlaid on a sun chart. You use it to see the shading around a spot and trace it on the sun chart, thereby calculating the effect of shade throughout a year. There are smartphone apps that do similar things. The Google Sunroof project is also really, really amazing, but its coverage is very limited right now.
As for degradation, panels lose about 1% productivity every year, so after 20 years, you should still be able to get about 80% of their initial power output out of them. Some manufacturers include this as part of their warranty, saying that after X number of years, the panels should still perform at Y wattage. However, keep in mind that some solar panel manufacturers don’t even last 20 years (it can be a cutthroat industry), so go with a reputable one that will hopefully stick around for a while.