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So you actually want like a "Remember me on this computer" option? This is actually unrelated to OpenID part. Here's a language-agnostic way how you can do it:
First create a DB table with at least cookie_id and user_id columns. If necessary also add a cookie_ttl and ip_lock. The column names speaks for itself I guess.
On first-time login (if necessary only with the "Remember me" option checked), generate a long, unique, hard-to-guess key (which is in no way related to the user) which represents the cookie_id and store this in the DB along with the user_id. Store the cookie_id as cookie value of a cookie with known cookie name, e.g. remember. Give the cookie a long lifetime, e.g. one year.
On every request, check if the user is logged in. If not, then check the cookie value cookie_id associated with the cookie name remember. If it is there and it is valid according the DB, then automagically login the user associated with the user_id and postpone the cookie age again and if any, also the cookie_ttl in DB.
In Java/JSP/Servlet terms, make use of HttpServletResponse#addCookie() to add a cookie and HttpServletRequest#getCookies() to get cookies. You can do all the first-time checking in a Filter which listens on the desired recources, e.g. /* or maybe a bit more restricted.
With regard to sessions, you don't need it here. It has a shorter lifetime than you need. Onl