To rescue or recover something from loss or destruction:
* Retrieve
* Reclaim
* Rescue
* Recover
* Preserve
* Save
* Reprieve
* Rehabilitate
To repair or rebuild something damaged or wrecked:
* Repair
* Restore
* Rebuild
* Refurbish
* Renovated
To gain something from something discarded or ruined:
* Scavenge
* Scrap
* Reutilize
* Recycle
To save money or resources by using something that would otherwise be wasted:
* Economize
* Conserve
* Maximize
* Optimize
Other synonyms:
* Remnant (used for salvaged goods)
* Wreckage (used for the remains of something salvaged)
* Derelict (used for something salvaged from a ship)
The best synonym will depend on the specific situation. For example, if you are talking about rescuing a ship from sinking, "rescue" would be a good synonym. If you are talking about rebuilding a damaged building, "restore" would be a better choice.