Here's a link
to a thread in which the first post is a letter from Berger discussing it for their VLD shapes. Most benchrest shooters I discussed it with say a 0.010" difference in seating depth is about the smallest at which they've ever been able to detect a difference.
There are several approaches to this. One is to try different depths with a load light enough to be safe touching the lands (about 10% below what is safe with the bullet at normal SAAMI COL). Then tune the load. Unfortunately there is an interactive dynamic, so another approach is to find an accuracy load, then tune depth to see if it gets still better, and if it does, then retuning the powder charge to see if it gets tighter, still.
In the 1995 Precision Shooting Reloading Guide, Dan Hackett describes how, in changing bullets to a 50 grain Nosler BT in his 220 Swift, he accidentally turned the micrometer the wrong way on his seating die and wound up with 20 rounds 0.050" off the lands instead of 0.020" off, as he'd expected would be best because, well, lots of people said so. To his surprise, this gun, which had never previously shot better that 3/8" 5 shot groups, turned in two 1/4" groups and two bughole groups in the 1's with that "wrong" seating depth.
As to velocity, that goes up very roughly as the cube root of peak pressure. So, a chronograph can give you at least some idea what the pressure difference is due to seating depth in your particular gun. Below is a graph taken off some very old 1965 data for a round nose bullet in .30-06. There is also a pressure plot on RSI's site showing a 6 PPC bullet's pressure dropping 20% in going from touching the lands to 0.030" off the lands. So this depends on bullet shape and position.
In the plot below, the study authors suggest the drop in pressure coming away from the lands (left side of plot) is due to increasing gas volume bypassing the bullet as it goes forward into the throat. When it finally is deep enough into the case, pressure rises again because the amount of space the powder is confined in gets small enough for the added confinement to overwhelm the gas bypass influence.
Obviously the exact depth at which you see these effects will depend on the freebore length in your chamber and on the capacity of your cartridge case and the diameter of the bullet, as that determines what percent of the powder space an additional 0.010" deeper seating depth takes up. In other words, the amounts vary dramatically with the particular cartridge.
I believe the Speer manual says they'd seen seating a 9 mm 0.1" deeper nearly double pressure. In a .300 RUM it might make 3 or 4% difference in pressure and maybe 1% difference in velocity.