Steer me in the right direction if you can please

I am building a web site for a company that wants to expand their home service from Houston to other larger cities in Texas. I understand that there should be a way for me to build one page that will dynamically insert user search terms into and render the page, as opposed to building what will essentially be a duplicate webpage for each city. (houston carpet cleaning, austin carppet cleaning, dallas carpet cleaning, and so on).

From a SEO standpoint what is best, and from a technology standpoint how do I do the dynamically generated web page and insert the relevant keyword? Can someone tell me what this process is called so I can research it?

Thanks for your help.

It's very simple, you either need a database of cities or database of user queries. After that, combine PHP with htaccess (mod_rewrite)

azureus3 is correct.