Putting a search box on your site which allows visitors to search your own site is an excellent idea. If your host supports Microsoft Frontpage extensions, then you can use the built-in search function. If not you can use a third-party search engine such as the one from Siteminer (which is excellent).
Unless you are writing a search engine, I would recommend against making it easy for your visitors to search the web from your site. You’ve worked hard to get them to visit you, so why give them a way to go somewhere else? Especially something like a search engine, which offers many opportunities for leaving.
If your site is of any size at all, you will need some way to make it easy for your visitors to find things. Some sites use a “site map”, which is more or less an outline of the site. I’ve seen this often with mixed results. If implemented well, it’s great. If not, it’s worse than not having anything at all.
A generic search box solves the problem of your visitor wanting to find something which is not obvious from your navigation menu. So I would recommend putting one on your site if it is of any size at all.