I have 20 sided dice which I would like to use to create a secure Monero paper wallet.
What procedure can I use to use the dice to create a valid mnemonic seed?
Is there any advantage of creating a 25 word seed instead of a 13 word seed?
The most straightforward way is probably to generate 256 bits of entropy (a fair 20 sided dice will give you a bit more than 4 bits per roll, so make it 64 rolls), and record all these throws in the custom entropy box at https://moneroaddress.org, then generate a new wallet from this.
You'll have downloaded this page first (it can run standalone from your hard disk, without internet access), and make sure the GPG signature checks out (there are instructions on the page).
Depending on your level of paranoia, you may want to do this on a computer that will never see the internet ever again.
This will get you a 25 word seed. 13 words seed are MyMonero's. The view key is derived from the spend key, rather than from a separate entropy pool. simplewallet still does this for deterministic wallets, but still uses the 25 word system for those. The simplewallet one is best, since MyMonero can import those too.
I personally would not trust a run of the mill D20 as the vast majority simply aren't made to roll in a genuinely random manner http://www.1000d4.com/2013/02/14/how-true-are-your-d20s/ http://www.dakkadakka.com/wiki/en/That%27s_How_I_Roll_-_A_Scientific_Analysis_of_Dice
If you are paranoid, then nothing less than truly random dice like those used in casinos will suffice (plus a nice padded area to roll them in as those buggers have sharp corners and can chip), as they are designed to prevent cheating. They can be purchased online. I have some myself.
If you absolutely, absolutely insist on using a d20, use it to add entropy to another random number generator, don't use it on it's own.