In OS X 10.10, with the new update to Safari, you can't simply reset Safari like before. Now you have to actually go in and manually disengage anything plugged in to safari.
This means entering the Library folders for both the system and user accounts affected by the Trovi/Conduit/Search protect redirect malwares.
First up is closing Safari down. Quit it, or Force Quit it using the Command/Option/Esc shortcut. Next up is to navigate to Finder and remove traces of the pest in your user files.
While some antivirus programs are great for this, avoid MacKeeper like the plague, it basically will do the same thing. Do not ever use it.
I should warn you, deleting files in this part may affect your computer adversely. When in doubt, TIME MACHINE BACKUP!!!!
Mouse up to the "Go" top menu selection, and hold down the Option/Alt key. Magically, the Library folder will appear, which you'll need to click on, and go in to. The file path should be something along the lines of /Users/YOURNAME/Library. Inside this are a few folders that you'll need to pop in and check out. Application Support is one of them, this will house anything dealing with preference files or misc files for programs or apps, including in some cases, search redirect add ons. Find the name of your assailant, be it Trovi, Conduit, or the plethora of others out there that hijack your browser (take note of the website it launches when you go to your homepage, check Safari's system preferences to double check prior to this dive into your system files).
Once you've located files associated with the program, Command/Delete them, or just delete them however you normally would. Securely empty the trash to ensure that even if they're in use, they will be deleted.
Next folder on the list is back in the Library, so head backwards in the File path and scroll down to Internet Plug-ins. Inside this folder is anything Safari uses, either intentionally or not. Clear anything in there that doesn't look right, this Folder is normally empty by default anyways.
Next folder for inspection is back in the Library folder, named Safari. This is the real bread and butter here, and where you'll find .plist files galore. You should open and clear Extensions folder, LastSession.plist, as well as the Local Storage folder. Do not delete folders in this enclosing Safari folder, only files.
Empty the trash securely again. Next up is to check the system Library folder for any lingering pest files. The filepath for this folder is simply inside the main drive, Library will be on the same hierarchy as Users, System, Applications, and so on. Open the Library folder, open Application Support folder, and again, check for anything suspicious. Anything inside this folder is a series of preference files for applications used by users/the system. Hopefully there should be nothing in this folder to delete, but on occasion you'll see Trovi or other folders in there.
The next folder to check, back up the ladder in to Library, is the Internet Plug-ins folder. This will contain files for you to delete, likely as .plugin files.
The final folder to check is back in the Library, called Preferences. This is where hunting and pecking will be a time consuming affair. You will likely have roughly 100+ files inside this folder, each of them is a com.whatever.whatever.plist file. These are pretty important files. Among these plist files will very likely be a trovi or conduit plist with a com.trovi.whatever.plist file name. Delete that little file, securely empty your trash.
The final process to finish this all up will be to set your homepage in Safari back to what it used to be. Open it up (WITH YOUR INTERNET CONNECTION OFF), go to your Safari preferences, input your homepage, then save that and close Safari. Restart the Mac, then turn on your Wifi/ethernet connection, and open Safari. It should be hijack-free.