The club website has information on how to buy shares in the team, but you may find your bank requires a little more information than what is provided there--especially if like me you have a bank that doesn't do this sort of thing terribly often. So here is all (I hope) the information you will require.
You can buy as many shares as you want, at €60.10 each (about $87). If you buy four or more shares, you are eligible to vote at the club's annual shareholder meeting. I believe only one person can own each share, so if you and your spouse wish to own a share, for instance, you either need to choose one of you that will own the share, or buy more than one so you can each have one. We might need to check with the club on that.
Your bank needs the address of the bank where the payment is going, which is:
Bancaja, Branch Vila-real-Empresas 585, Pl. La Vila, 8-1º 12540 Vila-real, Castellón, Spain
telephone (probably not necessary) (+34) 964 529 033
The beneficiary address is:
Villarreal CF, SAD
Camino Miralcamp S/Nº 12540 Vila-real
telephone (again, probably not needed) (+34) 964 500 250
The transfer information your bank needs is: IBAN ES 35 2077 0566 78 5100050965. SWIFT CVALESVV
IBAN is an interbank transfer code and Swift also gives some information about where the money is going. If you show this information to someone in a bank this should be sufficient to get the money where you want it to go.
Finally, don't forget to give your name and address and indicate that the transfer is for "purchase of shares" and indicate how many.
I am assuming the team really only needs your name since the shares will be electronic ones and your name will simply be listed on the share register, but I don't know that for sure!
So go ahead and become part of the Yellow Submarine officially and make Villarreal CF, quite literally, YOUR team!