How to make a small slam in bridge with only 25 high card points between the partnership?
Looking at just the East West hands without looking at the North South hands, 6D is a fairly poor contract.  It has only about a 20% chance of making unless you have peeked at the North South hands.

There are a number of choices that East/West can make during the bidding, but all of them should end up at 3N.

Possible auctions (depending on various subtle differences in partnership agreements and player judgement, all of which are playable) include:

1D-1N-2N-3N

1D-1N-2S-3D-3N

1D-2D-2S-3N (if not playing "inverted minors")

1D-3C(*)-3S-3N (inverted minors with a 3C mixed raise - I've also seen partnerships that use 2S or 2H instead of 3C for this purpose)

1D-3D(*)-3S-3N (inverted minors without a special mixed raise)

1C-1N-2N-3N

1C-1N-2S-3N

1C-1D-1S-1N-2N-3N



The calculation of slam success (thanks to Forget i was ever here) is as follows:


You need to guess who has the club Q so that you don't lose a club trick.  This is 50%.
You also need to avoid the diamond loser.  If the diamonds are 2-2, then you can ruff 2 hearts in the East hand.  There is another way to avoid a diamond loser, which is if the Q is singleton.  In this case, you need a heart finesse to work to avoid a heart loser, and whichever heart finesse you choose to try is 50%.  This comes out to 40% + 1/2*13%, so 47%.


Total odds are then about 50% * 47% = 24%.  This isn't exactly correct, as there are a few additional unlikely chances to make the contract as well as a few other unlikely chances for it could go down, but 6D is NOT a contract you want to be finding frequently.