The first thing you can do is ask them. Some places will even say so upfront on their websites.
On the broader question of how to spot a good rescue - some things to look out for include :-
Lifetime guarantee of taking the dog back if there are problems
A clear, upfront explanation of their homing policies. It's not fair on potential adopters if they fall in love with a dog on the website to then find out the adopter cannot fit the rescue's particular criteria. Typically, some rescues will restrict dogs going to homes with very young children, or where the adults concerned are out of the house for long periods. However, if you believe you can still offer a good home then it may be worth contacting them if you can show a well reasoned and evidenced case.
A thorough homecheck, involving everyone who lives in your house and any existing pets.
Dog will be spayed/neutered, microchipped, vaccinated, wormed, vet checked and will come with information on any known health issues, medications or ongoing care needs.
Dog will be behaviourally assessed. This is NOT always a perfect science especially if the dog has been in kennels, but if the dog has been in foster care then you will be getting a pretty detailed picture of their character. In particular, the rescue will be able to comment on the dog's suitability for living with dogs, living with cats/other pets.
The rescue will give you a realistic assessment of the breed characteristics, where appropriate. For instance, if you are looking at a greyhound, advice should be given on recall issues, prey drive, etc. If you are keen on a BC, you will be told about "herding" and asked if you can commit to a lot of exercise and plenty of mental stimulation. Huskies can't come off lead and often suffer from SA. This is the type of info you should be aware of and the rescue will be able to discuss with you honestly and openly.
During the adoption process, the rescue will be honest and reliable about communication and the adoption process. You will be given a clear timescale of what to expect, and the likely time between first enquiries and actually taking your new dog home. If you have very specific needs, like a cat friendly greyhound, this may well take longer but the rescue will be able to tell you this.
Once you have your dog, the rescue will keep in touch over the first few days to see how things are going. A follow up visit will take place once woof has been in for a few weeks. Many rescues organise fun and social events - charity dog shows, regular walks, quizzes etc. Supporting these will often be a great way to socialise with your new dog, but will also help raise funds for future rescue dogs.