Setup SharePoint Search Service
1. Central Administration -> Manage Service Applications
2. Select Search Service Application and click Manage in the Ribbon.
(If its not there, create it from New in the Ribbon)
From here there are tons of different aspects of search that can be configured, but for now I'll focus on the pure basics. And that's crawl, without crawling there isn't much to search on.
Start with setting up a daily crawl, on the Quick Launch on the right there is a link to Content Sources. By default your local SharePoint sites are added. From Crawl Setting click Create Schedules, create a daily schedule for Full Crawl.
This can be done for incremental too, but should have a much higher frequency, maybe every 15 mins or so.
You can start a Full Crawl right from the content sources by click on their drop down menu.
Adding a New Content Source
Lets say you have a file share with tons of documents, obviously that's what SharePoint is their for replace, but many still have it. Then you can add a File Share as a content source so its available from SharePoint Search.
Configure it:
Make sure that the user used to search have access to the file share, only read access needed.
Check Logs
Crawling generates logs that you can read to make sure their aren't any error etc. You can find the logs from the Quick Launch under Crawl Log.
Note: A common error when crawling SharePoint Sites when you have specified an URL in the search Start Addresses.
Access is denied. Verify that
either the Default Content Access Account has access to this repository, or add
a crawl rule to crawl this repository. If the repository being crawled is a
SharePoint repository, verify that the account you are using has "Full
Read" permissions on the SharePoint Web Application being crawled.
A fix for that error is found at Sensoft2000 blog.
Create the Search Center
Now the pure basics is up, but its enough to use the Search Center. You have probably noticed their is an Search feature already on SharePoint sites, but they only search within the Site Collection. Even if you only have one Site Collection on your intranet it will still exclude My Site where search on people are done.
Create a new Site Collection from Central Administration:
This Site Collection could be used on its own and you can connect your other Site Collections to use this Search Center when you use the search included on all pages.
Configure Site Collections to use the Search Center:
Here is an example of how it will look after you have connected it.