Explain How Vendors Make A Profit From Open Source Software?

They can sell ads on their websites.

Corporations that use open source software will still look for support options if the software will be used in critical systems. The other source is again from corporations that fund open source projects to further their development.
My company is building a solution using JBoss and purchased developer and software support.
Some companies also donate code (IBM and Sun have donated plenty of code to the Apache projects), some assign developers to further open source projects too. The interest is in community based development to reduce the single company investment in software that is similar across many companies.

tech-support licences and customizaton requests
see: RedHat
or else:
Sell the Reference Manual ( JBoss)
Sell a subscription of the documentation (CDN)
Sell the Installer (Out of the Box)
Sell Custom Software Development (CDN)
Sell Pre-Integrated Applications (JCorporate, RedHat ACS)
Sell “Enterprise” version. (WSAD, Sun Studio)
Sell Extensions (Instantiations, Embarcadero, SlickEdit )
Sell a Consumer Device (Tivo)
Sell Proprietary Software by improving Open Source Software (Poseidon)
Sell Code Management Services (Sourceforge, Sourcecast)
Sell Hosting Services (JCentric, WebApp Cabaret, EApps)
Sell an Application Service Provider (?)
Sell Conferences (JBoss)
Charge for changing the License (SOFIA)
Sue people using Open Source (SCO)
Publish books for Open Source (Oreilly, Manning, Wiley)
Sell A Book (Jason Hunter, Martin Fowler)
Sell Development Tools (see Adalon, Camino for Struts)
Sell a Magazine (Open source magazine)
Sell Business Applications (Compiere, Ofbiz)
Sell Speaking Engagements (NFJS)
Sell Open Source Migration Services
Sell White Box Hardware (Penguin)
Sell A Subscription Plan for Integrated Components (MyEclipse)
Sell A Network Appliance (SourceFire)
Sell Project Management Services (Assembla)
Sell Training (CDN)
Sell Adverstising (SourceForge, Javalobby, TheServerSide)
Sell A Proprietary Product, Advertise using Open Source (RefactorIT)
Sell Computer Time (Internet Cafe)
Sell Gaming Time (?)
Sell Proprietary Software built using Open Source Software Tools (Ant, JUnit, Eclipse)
Sell Proprietary Software Bundling Open Source Software (WebMethods, Cysive)
Sell Support and Maintenance Plans (JBoss)
Sell Certification (JBoss)
Sell Systems Administration Services
Sell On-Site Consulting and Coaching (CDN)
Sell Remote Debugging and Trouble Shooting (CDN) [duplicate of 34?]
Sell Open Source Application Specialized for a Particular Domain (Timesys for Realtime domains, Xemo for Music)
Sell Accessories ( ThinkGeek , JoyOfTech )
Sell Network Usage ( iMode )
Solicit Donations
Sell Glue to tie it all together (10xSoftware, platinum solutions )
Sell PDAs (Sharp)
Sell Cellphones (Motorola Linux based)
Sell Insurance (Open Source Risk Management)

They make profit the same way any software manufacturer does, in the way they sell it. Changes are made to make the the software something that they can copywrite.

They can advertise and gain money that way, or a lot of times they will ask for donations. If they really want your money, they’ll keep nagging you to donate in hopes that you will.

they will earn by selling plugins or adding some features
but the most common thing is they are giving that for as a service.