If you have a codex32-enabeld hardware wallet, simply collect sufficiently many shares and enter them into the wallet.
Alternately, go to the Documents link and download the booklet (either color or black&white). Read Section III.2 about Recovery to just get the instructions to recover your secret by hand. Read all of sections I and II to re-orient yourself.
If you don't know which tiles are missing, there is no efficient way to recover from this. You will need to try every possibility, trying the Error Correction process with each one.
If you do know which tiles are missing, you're in luck: you can use the Error Correction process to recover their original values.
The codex32 booklet is a secret sharing and checksumming scheme designed to store Bitcoin secrets redundantly and with high assurance of data integrity, without the use of electronic computers. Before beginning the recovery progress, we strongly recommend that you download the booklet and read through it. It is about a 10-15 minute read.
Next, you will likely have one or more "shares" which encode the share data. These will be identifiable because they begin with the characters MS1. The next character will be a number, probably 2 or 3, which indicates how many shares you need.
If you have fewer than the necessary number of shares, there is nothing you can do. You need to locate more shares.
In all likelihood, you do not wish to recover the coins, but only verify the integrity of the shares. You can do this without the use of electronic computers, which means that you do not need to worry about loss of coins due to technical mistakes or malicious hardware. To do this, you only need to:
If you have enough shares, and you want to recover the coins, first obtain a codex32-enabled wallet such as a [FIXME no such wallets exist]. If the share(s) are accepted by the Bitcoin wallet, and they show a nonzero balance, you are done.
If the wallet accepts the shares but shows a zero balance, it is possible (though very unlikely) that the shares are incorrect. You may wish to try with a different set of shares. More likely, the user of this scheme layered on an additional, nonstandard, scheme for Bitcoin storage. Hopefully they left some additional documentation, or else you have a job of reverse engineering ahead of you.
If you need further assistance, such as if the shares do not start with ms1, you may wish to contact pearlwort@wpsoftware.net to arrange a phone call, for a reasonabe fee. Pearlwort offers only technical advice and makes no claims or implied warranty whatsoever, including that he is able or willing to recover any amount of funds.