If you like Caroline G fair enough, but it's a stretch to call that strength training. It's cardio with weights, and it's more effective for general fitness and weight loss. It appeals to people when they're really motivated because it's intense, high energy and leaves you shattered, 'feeling the burn' afterwards. But it isn't the most sustainable programme long term. It's also too intense for many people, meaning risk of injuries, especially when exercises are done at speed.
Strength training is slow and plodding. It shouldn't leave you feeling exhausted afterwards. It gets your heart rate up, but only for a few seconds as you then rest in between the exercises. That rest is important - strength training taxes your central nervous system as well as your muscles, you need time to reset.
Stronger by the day that someone mentioned up thread is a paid programme, but one of the best that I've seen for getting women into strength training. Mainly because it has a prequel - before the barbell - that helps you before you feel ready to go to the weights section of the gym - but also because it has videos to explain every exercise and it offers you similar substitutions if you don't want to do a particular exercise (eg due to injury)
Having a PT is ideal though expensive - however if it's doable, a PT once a week for 3 months would give most people enough knowledge and understanding to carry on on their own if they needed to.
Strength training can be done bodyweight at home, but it is much harder to progress doing it that way for most people.