Here is the method that Nathan Winograd puts forward and has used to make high kill shelters into NO kill shelters. All information on this post is from that site.
Also on that site are many helpful links to pdfs that you can download and print out to use with your local shelters. Please take the time to go look!
The very first step is for the shelter manager to honestly consider all ten steps and make the commitment to put all the steps to work and REALLY mean it. The manager needs to say "TODAY this minute I decide that NO more healthy, adoptable animals will die on my watch" THEN do it! It is not easy to change the way a shelter has run for years but it can and has been done. By the shelter manager leading the way the staff will also start to find ways to save the animals instead of just killing them - the easy out. No killing is not easy for most but it is the quickest way with the least amount of work to empty cages. All the ten steps require doing things that most shelters do not do and changing their view of the public and of rescues. Shelters ARE responsible for deciding to kill the animals in their care but without the public and rescues they will never be able to stop. To save animals WE ALL have to work together. None of us are perfect and we all have a part in the number of animals dying in shelters. But only the shelter managers can STOP killing the animals that are left in their facility. We the public and rescues can only do so much without the shelters committing to stop the killing. It is their finger on the plunger.
So what is this method??
Here are the 10 steps
1 Compassionate Director
2 High volume, low/no cost spay/neuter programs
3 Foster care
4 Comprehensive adoption programs
5 Medical and behavioral programs
6 Pet retention programs
7 Trap neuter release programs
8 Rescue groups access to shelter animals
9 Volunteer programs
10 Public relations and community involvement