This would really depend on the individual, as well as on the individual's goals. For example, if someone was overweight, not used to training and significantly wanted to reduce their body fat percentage, then I would suggest that they should start by doing more cardio with only 1-2 heavy resistance sessions per week.
Although resistance training also burns fat, certain types of cardio may be more suitable in the beginning phases of training as it helps that person get used to building up a sweat, getting their heart rate up, getting comfortable with exercise and generally does not require as much skill as weight training, so it's good for a beginner or someone who has not been into a gym in a while. If someone was lean and wanted to tone up, then I would suggest that they minimise the cardio.
For the majority of the population though, I would suggest that they should be doing some form of weight/resistance training 3-4 days per week, but never more than two consecutive days in a row as you need to give your body a chance to recover. The reason I suggest this is because the majority of proven workouts base their training on this ratio.
This does not mean that you have to hang out in the squat rack four days per week doing eight reps over and over again as that can get boring, you can mix it up with weighted circuit training, body weight HIIT, a strength class etc.
So in answer to the question, everyone is different, so for some people the above ratio would be fine, however for the majority, I would suggest that they should be adding more resistance sessions into their week.
How many times a week should we be trying to resistance train?
Three to four, ideally. Try to avoid doing heavy sessions two days in a row and ALWAYS have a rest day each week.
If I love cardio but find strength training really tough, how can I fit it in more often without dreading it entirely?
I would suggest adding cardio into your strength workouts, doing a hybrid workout (half cardio and half strength in your designated training time) or even setting up a circuit with light weights on some days, so you are still enjoying cardio, but you are also getting the benefits of weight training.
If you are in the gym, perhaps you want to start with 15 minutes of interval training on the treadmill or bike, followed by a circuit where you do 5-7 exercises consecutively, followed by a 400-metre sprint at the end of each set. That way you still get to enjoy a fast-paced workout, but you're also getting the benefits of resistance training.
If you wanted to do a heavier workout day, perhaps after you finish your 3-6 sets of each exercise, you add in a cardio exercise such as one minute of burpees/running/bike before moving onto the next exercise.