There are two ways to put a search engine on your site:
1. Build Your Own
2. Use a third party search engine, (ex. yahoo, google).

I recommend using a third party search engines, because it will also increase your page rank, or show supplemental result in their searches!

Here are the ways in brief:

Build Your Own:
There are two ways to build search engine for your site.
1.) Use Search Engine Builders: There are many companies which provide search engine builders. But this method is difficult & costly also.
2.) Build Your Own with your knowledge: If you are having such a good knowledge then you must not look for it here.

Third Party Search Engine:
There are many groups which provide you with such a good search engine for your sites. I will be mainly discussing about the most popular groups.

It must be noted that Google robots, crawl your site very late. Even after three months the launch of Digital Technology, Google has not crawled this site. Well it also depends your progress. The more number of sites links to your blog, your blog will be indexed early. If you have started a new blog you must consider Yahoo Search Engine first, but if your blog is being indexed by Google then you may surely go for Google search.

Google Search Engine
As you know Google is one of the best search engines in world. It offers its magical search engine for your site. Google offers its search functionality with its other product named as Google Adsense. If you want to get Google Search on your site, you must follow the following steps:-
1. Go to Google Adsense & register there.
2. Go to Adsense Setup.
3. Follow the simple steps there.
4. Get your code & put it on your site.
5. Your search engine will begin as soon as google robot crawls your site.

Yahoo Search Engine
Yahoo has not integrated its search engine with any other program. Also its robots crawl your site at regular intervals. If you want to get Yahoo Search on your site, you must follow the following steps:-

1. Go to Yahoo Search Builder.
2. Login with your Yahoo account or Register there.
3. Follow the simple steps there.
4. Get your code & put it on your site.
5. Your search engine will begin as soon as yahoo crawls your site.