Dovetailed sights are typically cut with a very slight taper and TYPICALLY come out from the left to the right as viewed from the rear with the muzzle pointing away.
Lay the gun down so that the left side (as viewed from the rear) is on top and rest the gun on a solid but non-marring surface. A thin block of pine wood works nicely. You want the barrel to be supported so that it lays flat and is solidly in contact with the block. It sometimes helps if the muzzle hangs slightly off the end of the block so that there is room for the sight to come out.
A brass punch is used to drive the sight out of the dovetail. The tip of the punch should be held on the dovetail portion of the sight and not higher up on blade. Use a substantial punch, not a fine tip. Just make sure the tip of the punch is acting entirely on the sight and not the barrel. I'm right handed so I tend to use the blade of my left hand to pin the barrel flat against the bench block while holding the punch in position with my left thumb and forefinger. I use my right hand to hold the hammer. You're not driving a railroad spike but don't be afraid to whack the punch a bit. The sights can be rather tight.
Once you get the sight to move a little, they usually come out pretty easy.
A little Hoppes #9 and Q-tip will remove any brass markings you get on the sight.
Installation is reversed, flip the gun over and drive the sight in from the direction it came out. Put the sight back in generally the same position (usually centered in the base) and fine tune its position if needed.
Make certain the barrel is supported, you don't want to be applying force to the cylinder when the gun is laying flat. You can also pull the cylinder out of the gun to make it easier to pin the gun flat on the block.
You can buy plastic bench block that has holes and V's cut into it but an excellent poor man's bench block (and my favorite) is a hockey puck with a hole drilled in the center.