if you do not want to install sql server to your clients' computers, then you should develop your application with portable database solutions such as sqlite. It is a database system developed for the situations that fit to your case :
https://www.sqlite.org/[
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There are .net adapters for sqlite as well, therefore there is not much of a change in your code while converting it to the latter:
http://system.data.sqlite.org/index.html/doc/trunk/www/index.wiki[
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If you insist on microsoft sql server, the most you can do is to prepare a bootstrapper installer that will also install MS SQL Server Express edition (which is free). But be warned; the installation requires some knowledge on databases (person installing will determine sql instace .etc.
Here are some examples on implementing sqlite.net:
Using SQLite in your C# Application[
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https://code.google.com/p/sqlite-net/wiki/GettingStarted[
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http://zetcode.com/db/sqlitecsharp/[
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http://www.dreamincode.net/forums/topic/157830-using-sqlite-with-c%23/[
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