I've just purchased a replacement gasket for my Silvia but I am confused as to how to replace it. I removed the screen and expected to be able to remove more parts so that I could more easily get to the old gasket. Is there a technique to removing the old gasket? I can't seem to figure out how to get it out without prying at it with a screwdriver. Does this sound right?

Any advice appreciated.

Poke the gasket with an awl and pry it out.. it is simply pressed into a groove. You may also be able to pry it out with a thin screw driver or similar implement. Some gaskets have a small dimple in the side of the outer perimeter (usually three or four), you might be able to pry easier here.

If your gasket is old or dried out, it may come out in pieces and with some difficulty, hopefully not.

jesawdy wrote:Poke the gasket with an awl and pry it out.. it is simply pressed into a groove. You may also be able to pry it out with a thin screw driver or similar implement.

EEK! Don't pry! The gasket lives in a channel of soft brass, and prying will gouge the channel, and the gasket may fail to fill those gouges, and you now have a place for water to leak around the gasket.
One trick that sometimes works is to (and you may want to do this cold so you don't scald yourself) lock in the blind PF, and turn the machine on, turn on the brew switch, and slowly back the PF out. Sometimes the water pressure behind the PF will work its way under the gasket and the gasket will follow the PF handle out. If this doesn't work (and give it a coupla tries) then you can us a simple drywall screw or two. Drive them in just past the point, and pull he whole thing out with pliers. Or whatever parts come out with the screw. It may take a coupla tries, depending on how long its been in there. If you don't have drywall screws handy, ask your favorite construction guy, theatre guy, or hardware store. They're usually sold in bulk, by the pound, and they may be able to figure out what to charge for a couple.
Be careful of the soft brass parts!

Easy E61 grouphead gasket removal elaborates on Chris' suggestion and a few other grouphead gasket removal tricks that apply to most espresso machines.