I've developed an application in vb 2010 and my back-end is sql server 2008. What are all the softwares i need to install in the client machine ?

2 things you should take care of:
1) in your project publish settings, when the user install your application the "application files" and "prerequisites" will be automatically installed on the user machine
so make sure you include everything in the application files
2) the user machine platform
if the targeted machine is 64bit platform,you should assign your app to 64bit
but if its a 32bit platform dont do anything
if you want both platform(64bit and 32bit) assign your app to X86bit
go to Build - Configuration Manager - Active Solution platform - new - new platform select X86 or X64bit
good luck

Sorry.. I think I've not presented my query clearly..
I'm talking about Client-Server in a LAN Environment.
My database will be in main Server PC say PC1. I want Client PCs - PC2, PC3 to connect to this DB in PC1. For this, I need to know what are all things i need to install in PC2, PC3, etc.
i.e whether VS 2010 is must to install in the Client PCs viz PC2, PC3, etc.
whether Sql server is must to install in the above ?

oh ok..then you dont need to install anything just create the installer for the PCs and set up the right directories and you're good to go.

create the installer for the PCs and set up the right directories

How to do it ? Can you explain me please ?

go to your project properties >>Publish >> Publish Wizard..