I recently bought a new laptop with a web cam build in but it doesn't work when I want to show myself to my friend on messenger

Once your webcam is working on your computer,you can configure it to Yahoo Messenger.
YAHOO SPECIFICATION
To find out what the requirements are for messenger webcams and automatically download the latest control software , check out the following.
http://help.yahoo.com/l/us/yahoo/messenger/messenger10/webcam/mstacamtest.html
You have to Use Internet Explorer for that.

Note
Its good practice to disconnect and re-connect your webcam before you start - if you have been using it elsewhere the Yahoo software may have difficulty in locating it, and you can get a 'webcam not located' or 'webcam being used in another program' error message.
Mine, I just unplug it from the USB and plug it back in, if yours is integral with the computer you will have to re-start the computer, use the keyboard shortcut or disable / enable from the Device Manager.
Of all the chat programs, Yahoo is the most painful software to set up but if you follow these instructions you should be ok.

INTERNET CONNECTION
Webcam connected
Open messenger - on top toolbar. Left click ( > ) Messenger > Preferences > Connection - Select 'no proxies' or 'connect direct to the internet' depending on the version of messenger you have
make sure your internet connection and country are correct in the lower two boxes > Apply > OK

TESTING
> Messenger > My webcam - the warning panel will launch, click 'OK' and your webcam will start. You should be rewarded at this stage with your happy smiling face.

DEFAULT
With webcam still running > Messenger > Preferences > Webcam > Camera Source - set your webcam as default using dropbox. > Camera Settings - adjust settings to suit. > Apply > OK
Take a note of any additional software, if you have multiple choice for Camera Source, you may wish to uninstall any redundant webcam software later to prevent conflicts

PERMISSION OPTIONS
> Messenger > Preferences > Webcam - make your selections ( who you will allow to view you) > Apply > OK

IN USE
When you are both on line and wish to show your webcam > Actions > 'Invite to view my webcam'. This will launch an invitation on your contacts screen when they 'Accept' your webcam broadcast will start- There can be considerable time lag ( 1 minute) before they see you, so dont be too impatient ( You can check the status on the bottom left of your webcam panel. You can 'drag and drop' the frame to a convenient location by grabbing the top border.
There is a shortcut ( webcam icon ) down by your pic as well
Your contacts may need to configure their connection the same as INTERNET CONNECTION above or they may get a "webcam not connected" message