Once you know that the reason your dog is holding up that paw or limping is a ligament injury, you will need to decide how to approach the problem.  To make the best decision you need to carefully consider the facts about treatment options & vets' recommendations.
Unfortunately it is very common for vets to recommend unneeded surgeries for ligament injuries.  The reasons why this is so are considered on the page 'Looking Deeper Into Surgical Recommendations'.  (on the navagation bar at left)    
---- Nevertheless, it is true that some dogs with these injuries do need surgery to recover, so the question that must be answered is "How can you tell if a dog needs surgery or is going to be able to recover without surgical intervention?"
---- There is no doubt that it is best to avoid surgery if it is not needed.  Don't agree to surgery because you have been told by a vet that the surgery he recommends has an outstanding record.  This is simply not true.  Surgery is necessary when the dog cannot stabilize the joint non-surgically, but surgery is not a shortcut to a superior recovery.  All the surgeries for these CCL injuries have significant risks of complications and poor outcomes. Statistically, the results of the surgeries are far from impressive. Surgical treatment very seldom results in a better recovery than a non-surgical approach. However, if non-surgical methods are not effective, it is best to try surgery.  But bear in mind that the surgeries available for this problem are not miracle treatments.  They are all far from ideal.  While many surgeons claim to have excellent history of success when they are talking to clients about the surgery they sell, independent studies of the actual long-term outcomes make it clear that these surgeons' claims are closer to being sales pitches and false boasts than accurate descriptions of the results dogs experience. 
After considering the course of thousands of successful non-surgical recoveries, I came to the conclusion that almost all dogs who can recover without surgery will show that they are re-stabilizing the joint beginning within 8 weeks of carefully restricting activity.  Their symptoms will slowly improve, and they will have slow ongoing improvement thereafter. 
---- That is the treatment choice that makes sense.  Restrict activity carefully and see how the dog does.  You must be careful about doing the restriction properly, and you must be patient. 
---- If Fido is not improving after 8 weeks, the next step for most dogs should be a custom-made brace.  The brace will hold the bones in proper alignment while Fido's body builds the permanent fibrous scar tissue stabilization.  There is a section about braces on the FAQ page here at this website.   
---- If careful restriction including brace use is still not effective in re-stabilization, conventional stabilizing surgery will be appropriate.
NSAID drugs (Non-Steroidal Anti-Inflammatory Drugs) like Rimadyl, Deramaxx, Metacam, etc, are commonly prescribed for dogs with ligament injuries.  While these drugs are useful in relieving the pain and reducing the swelling that accompanies a sudden traumatic injury, there are good reasons to minimize their use.  Please see the FAQ page here at this website for more information on this.
"But Max, the vet told me that if I don't have surgery done immediately Fido will be crippled with arthritis, and the other rear leg's joint will fail from having to carry all the weight.  He tells me I can't wait 8 weeks to see how Fido does ..." 
---- Vets who want to sell you surgery will often distort the facts or simply lie about treatment risks and results.  Statements that are intended to rush you into agreeing to surgery are misrepresentations designed to use your love for your dog and your desire to do what is best for Fido together with your trust in vets to sell you on a high-profit procedure.  A ligament injury is not an emergency.  If you restrict your dog carefully it is likely (not certain, but very likely) that you will see symptoms begin to improve and slowly continue to improve as Fido re-stabilizes the joint.  The careful restriction prevents high stresses to both the injured joint and the other rear leg's stifle(knee) joint.  High stresses from running/jumping can cause further injury to the already injured joint or the contralateral stifle joint, but Fido's activity being restricted will protect both stifles against further injury.  We hear about a great many of these injuries and recoveries. Injury to the other rear leg during recovery from the original injury is rare. Vets who are promoting unneeded surgeries often use the false claim that dogs are going to injure the other rear leg unless they have immediate surgery as a sales tool to push people into agreeing to surgery. Actually there is only a very slight danger of this happening. The greatly reduced stresses on the legs make the 8 weeks of diagnostic restriction safe.  (By the way, surgery also requires restriction of activity, so agreeing to surgery does not relieve you of that.)
---- It is true that many dogs do have similar injuries to the other rear leg after the original injury.  About 40% within 2 years.  But this is true whether or not surgery is done.  Ligament injury in the other rear leg is unlikely to occur during the time the dog is properly restricted simply because the stresses on the joints are greatly reduced by the activity restriction. 
---- In all dogs who have ligament injuries, the increased risk of the other rear leg having a similar injury in the future is largely a result of the two rear legs having the same genetic predisposition to this kind of injury and the same influences (early neutering, for example). Dogs who have surgery do not have less risk of injury to the other rear leg than dogs who do not have surgery. 
"The vet says Fido may seem to improve with restricted activity but he will just get worse again later ..."
---- It is true that a dog can improve but then may re-injure the joint later.  This can easily happen when people restrict activity for a time but then allow too rapid a return to normal activity when improvement is seen.  This is not a failure of the non-surgical method.  It is a failure to carry out the method correctly.  The proper way is to slowly & watchfully increase activity over a number of months.  This lets the joint gradually build up the tough fibrous new support that stabilizes the joint.  There are vets who advise people to restrict the dog for 6 weeks or 8 weeks and then, when the dog is improved at the end of that time, tell the people to let the dog resume normal activity abruptly.  This too-rapid increase in stresses on the joint often results in re-injury.  A surgically-inclined vet sees this and says "See! Non-surgical recovery doesn't work!"  But it was failure to allow the time needed for the joint to build & strengthen the stabilization that was the problem.
---- The right way to manage a non-surgical recovery to prevent re-injury is described on other pages here at this website.  Basically it is gradual activity increase over a number of months. 
---- Surgery has become the preferred approach of many vets not because surgery is better for dogs, but because it is better for vets.  There is little income for a vet in recommending careful activity restriction.  A TPLO on the other hand takes about an hour to do and yields several thousand dollars profit above costs.