The basic process is to submit the fairly simple paperwork that makes the appeal, within thirty days, and follow instructions after that, including timely submissions in response, and then show up for the IAD hearing and state the facts including your reasons for being outside Canada or otherwise for not returning to Canada sooner.
The costs for that are incidental, including mailing costs, document copying costs, and other incidental fees.
The costs go up dramatically if a lawyer is hired to help. Better to have a lawyer.
But it is not necessary to have a lawyer. It appears a high number of those who do appeal do so without being represented by an attorney. But no advanced degrees in mathematics necessary to calculate the odds are better when represented by a lawyer who can help you present your case more persuasively.
Some numbers: Actual statistics are hard to come by. I am aware of the 2014 numbers. 1008 PoE Departure Orders appeals decided, and as I recall just 77 of those resulted in keeping PR status. General reports indicate less-than-ten-percent are successful in keeping PR status after being Reported at a PoE. But I think that is based on percentage of successful appeals. For example, 1408 PRs were issued 44(1) Reports and Departure Orders at a PoE in 2014. Again, as I recall, I believe only 77 PRs succeeded in saving PR status that year.
There are indications the trend has been toward increased PoE scrutiny and elevated enforcement, and overall Canada appears to be getting more strict (albeit not strict enough more than a few here complain) at every stage, including the IAD. That said, since we do not know a lot about the actual numbers, it is possible that they are, so to say, catching more returning PRs in breach at the Ports-of-Entry, in large part due to the implementation of enhanced technology and better record-capturing and database-accessibility, and the apparent trend is not about getting more strict in terms of criteria applied in deciding who gets reported.