I want to Upgrade Dell Inspiron 620s For Gaming

It is not possible to upgrade the Slim Desktop.

you are limited by the tiny power supply and the tiny amount of room for a graphics card ... you would get a small jump in performance if you replaced your HD 6450 with something like this low profile r7 240 ... you would get to play at low settings ... it's the difference between the 64bit memory interface in the HD 6450 and the r7 240's 128mb memory interface.

I know about space issues but

it is possibke to improve space by changing CPU cabinet but i don't have any idea about how to improve power supply

Please suggest me what changes i have to do for improving  my power supply

And which mother board will work with inspiron 620s configuration

Sorry for my questions i hav3 very little knowledge about all these things...

Is it possibke to improve space by changing CPU cabinet but i don't have any idea about how to improve power supply

Please suggest me what changes i have to do for improving  my power supply

And which mother board will work with inspiron 620s configuration

Sorry for my questions i hav3 very little knowledge about all these things...

What is your overall budget?   Which core i5 CPU do you have now? how much and what speed memory? 6GB is odd...

I think the 620S motherboard is micro ATX. Lots of cases that will fit that but the challenge is getting the power buttons and front panel connections to all work.  

An low-end case is $30-50. I have a rosewill line-M that I use for a Linux system and it was $32 on sale shipped from amazon. prices fluctuate. Looks like it is $41 today. It is a decent case, but very basic.

http://www.amazon.com/Rosewill-Micro-ATX-Computer-12-5-Inch-LINE-M/dp/B00AAJ0ZGK 

If the Dell MoBo has screw mounts in standard locations mounting it should be easy. If not you would need to move the mounts (called standoffs) in the case. Not hard but you need a small drill and some patience. That case comes with extra standoffs and lots of screws.

Power supplies will become a debate on its own. Lets just say for example this one: which is $30 after rebate.

http://www.newegg.com/Product/Product.aspx?Item=N82E16817438012

so for $70 to 80 you could have a case and a PSU that will handle a larger graphics card.

Add in a $100 to $200 graphics card and it would be an OK system. 

You should compare the cost to update your current system with the cost to building a better one and sell your current one.

Your money would be better spent finding a OFF LEASE Precision T3500

on Ebay or at Walmart or Microcenter etc.

http://www.ebay.com/sch/i.html?_nkw=precision+t3500

 Dell Off Lease REFURBISHED Precision WorkStation T3500 2.8GHz XQC 8GB 160GB DVD Win 7 Pro Tower Computer

 Keep in mind that WIN7 or WIN8 the Home version is $109 and the Pro version is $199 and Ultimate is $399 just for the software.