There are three ways to interact with the search system:

Specifically for searching nodes, you can implement nodeapi ('update index') and nodeapi ('search result'). However, note that the search system already indexes all visible output of a node, i.e. everything displayed normally by hook_view () and hook_nodeapi ('view'). This is usually sufficient. You should only use this mechanism if you want additional, non-visible data to be indexed.

Implement hook_search (). This will create a search tab for your module on the /search page with a simple keyword search form. You may optionally implement hook_search_item () to customize the display of your results.

Implement hook_update_index (). This allows your module to use Drupal's HTML indexing mechanism for searching full text efficiently.

If your module needs to provide a more complicated search form, then you need to implement it yourself without hook_search (). In that case, you should define it as a local task (tab) under the /search page (e.g. /search/mymodule) so that users can easily find it.