I've written recently about main points on migrating from Windows to GNU/Linux. Those reasons included one which pertains to the software included with the GNU/Linux distributions, and replacing those proprietary products with those on GNU/Linux that you will never need to re-buy or pay upgrades for again in the future. But how is this done? With time and patience, which not everybody has. But if you do, it will pay off dearly over the years you stay on the open source road. One warning though, migrating is not for the timid, it IS a lot of work.
Where do you start? As I've pointed out before, I highly recommend changing the operating system over to GNU/Linux, and either use Wine or VirtualBox if you need to continue using Windows applications. If you are just starting to migrate, this is probably going to be the case as it does take time to locate new applications and migrate over to them. There may be some temporary time where you need to run Windows applications alongside with the GNU/Linux applications. Others have suggested dual booting the PC but I prefer to run GNU/Linux and use everything from within it because you can run concurrent applications and operating systems (with VirtualBox) at the same time, and easily switch back and forth between them if needed.
Finding open source and GNU/Linux applications to replace the proprietary Windows applications is the first step. There are several lists available if you Google them. And if you look at them you will notice that they are very similar which may help to narrow down the best fitting application for each purpose. I am including my top choices below based on my experiences of migrating not only myself but many others from Windows to GNU/Linux, pointing out the purpose, the old Windows application and the GNU/Linux replacement for each. As with most open source, there can be an array of choices for each proprietary application, and I've ended up trying out each one and picking the one I liked the best.
Office Suite: Microsoft Office -> OpenOffice / LibreOffice (LibreOffice is a fork of OpenOffice)
Project Management: Microsoft Project -> Project Management (Planner for Gnome)
PDF Creator: Adobe Acrobat Writer -> Cups PDF Writer
Font Management: Adobe Type Manager, Suitcase -> FontMatrix
Video Capturing/Editing: Adobe Premier -> Kino, Cinelerra or OpenShot
Desktop Publishing: Adobe Pagemaker, Adobe InDesign -> Scribus
Graphics Editing: Adobe Photoshop -> GIMP (GNU Image Manipulation Program)
Visual HTML Editing: Adobe Dreamweaver -> Kompozer
Vector Graphics Editing: Adobe Illustrator -> Inkscape Vector Graphics Editor
Audio Editing: Adobe Audition -> Audacity
Virtual Machine Manager: VMWare Workstation, Microsoft VirtualPC -> Oracle/Sun VirtualBox
Archive Management: WinZip -> Archive Manager (File Roller for Gnome)
Code Editor: Notepad++ -> GEdit
FTP Application: WS_FTP -> gFTP
IRC Application: mIRC -> XChat IRC
Scanning Software: Proprietary scanning software, or Windows Imaging -> Scanner Tool (xsane for Gnome) or Simple Scan for Gnome
DVD Authoring: ULead DVD Movie Factory -> DVD Styler
Audio Playback: WinAmp -> Rhythmbox
CD/DVD Burning: Roxio CD/DVD Creator -> K3B
Video Playback: Windows Media Player, Quicktime Player -> Totem and VLC
Label Creating/Printing: Microsoft Word -> gLabels
For the list above, the GNU/Linux applications provided enough functionality to get up and running, and in a lot of cases, provided additional functionality that was missing before (for example VLC can play a huge array of file types yet Windows Media Player had problems with many non-Microsoft formats).
Migrating any existing data files is the challenging part, as existing data may not necessarily open in the GNU/Linux equivalent software. Sometimes, data may need to be recreated, in the case of Scribus which cannot import proprietary file formats from other desktop publishing applications like Microsoft Publisher, QuarkXPress, Adobe InDesign, etc. However other applications like Inkscape can open Adobe Illustrator files, and OpenOffice/LibreOffice can open/write Microsoft Word/Excel/Powerpoint files.
Other applications like Mozilla Firefox, Thunderbird, Sunbird, KeePassX, etc are 100% cross-platform so that the applications are practically identical between Windows and GNU/Linux and there is really no difficulty in migrating with them. Data is found and opened, and most if not all settings remain in tact.
I've also discovered new GNU/Linux applications that are excellent for additional purposes, that I did not have in Windows:
Genealogy: Gramps Genealogy System
Digital Photo Management: digiKam
MP3 Replay Gain application tool: easyMP3Gain
MP3 Bulk tag editor: EasyTag
CD/DVD content cataloging system: GTKtalog
File backup / synchronising utility: rsync
Many of these packages are included in Fedora, which is my primary GNU/Linux distribution choice. There are a couple however, that I've had to seek out 3rd party RPM packages and install them that way (easyMP3Gain and GTKtalog are two of them). The examples above are just scratching the surface of what is available, it's up to the user to do the research and find them. Which proprietary software have you replaced and with what?