I don't have any evidence that keeping them extra dry makes them last any longer, but I bought a pound of silica gel (for drying flowers). I keep a litle paper packet of silica gel as a dessicant inside the plastic peanut-butter jar where I store pepper and tomato seeds ... in the fridge.
Necessary? Probably not, since so many people have good success just drying them first, and then storing them sealed. But it reassures me.
And the humidity indicator cards show that the silica gel IS keeping the humidity lower than it would be otherwise. It shows the RH as around 10-15% when I've changed the desicant bag recently, and it takes an hour or two to reduce it from around 30% when the jar has been open a while.
One bag lasts 4-8 minths, depending on how often I open the jar. And you can regenerate the silica gel by baking for a while, at 260 F.
Some people use dry rice, baked extra-dry, as a gentle dessicant. Bake it not-quite-brown-yet.
Everyone else was giving good, simple, practical advice, so I had to contribute some unecessary complexity! The only practical aspect is: get them GOOD and dry before sealing them up or freezing them.
When I asked a local Master Gardener about dessicating seed for storage, she hadn't heard of the idea. When she consulted with her buddies, their consensus was that, if seed was dry enough to snap or crunch when you bent or crushed it, it was "dry enough".
If you ever manage to get a seeds internal humidity down to zero, you would kill it.
P.S. Another way to tell how dry your jar of seed is, is to store a piece of newsprint inside. After a few weeks, if it feels limp, it may not be dry enough. If it is crisp or brittle, it is plenty dry.
