I can't tell you how many times people come into my office and say "I just don't get it; I exercise an hour every day and watch what I eat, and I just can't lose weight!".
Exercise is great for the body - it is fantastic for building muscle, for improving mood, for balance and strengthening, and really healthy for the heart (great drug free way to lower blood pressure). Weight lifting and weight bearing activity can strengthen and protect bones from osteoporosis. Yoga and tai chi can improve strength, balance, and flexibility as well as help core muscle strength and back pain issues.
Aerobic exercise - running, biking hard enough to get increase your heart rate up has been proven to boost the size of the hippocampus (the part of brain used in memory and learning) and helps us keep our memories, even when fighting dementia (Harvard). This is especially beneficial now when a new case of dementia is diagnosed every 4 seconds globally. A regular exercise program can also improve mood in people with mild to moderate depression and plays a role in treatment of people with severe depression (Harvard article).
With all that exercise does, it is very beneficial and should be done. It is just not the key for losing weight!
You could run an hour per day and burn 300+ calories, but at the end of the month that is about 9000 calories, which is not worth even 3 pounds of fat loss. Study after study has come out showing that you cannot outrun a bad diet (BMJ article; dietdoctor). This doesn't mean you shouldn't exercise, just that you shouldn't use it as a way to justify your diet.
If you do want to start exercising regularly here are some programs you can try to slowly build up to regular activity:
Push ups are some of nature's perfect exercises - they improve core muscle strength as well as upper body. If you can't do push ups on the floor, do them against a counter top to start, or even against a wall! 30 day 50 push up challenge
Running or walking can get you good aerobic exercise - you just have to do it fast enough to get your heart rate up.
This is a good starting program for people who are not fit.
Guide to becoming a runner (later in life/safely). I have never been a runner, but I did this challenge last fall and got to where I could run 4 miles 3 times per week before it got too cold - I am starting again this month!
If you're looking for higher intensity then look into a HIIT program (High-intensity Interval Training). These programs maximizing your exercise in a shorter time by put together the strength training with the cardiovascular workout. I have not tried any of these, but there are a number of programs online. This one appears good for beginners: (3 HIIT workouts for beginners).
Regardless of what activities you decide to do, it is a good idea to first focus on diet when you are making a change. Adopt the LCHF lifestyle for 1-2 months before even worrying about starting a program. Then, when you decide to start activity, start something that is mildly challenging at first to get used to regular activity, then increase intensity as you are able. (5 steps to starting exercise, Mayo Clinic). Showing yourself that you are making progress is important. Make a goal: try to exercise 3 times per week to start, or maybe you want to able to walk up stairs without shortness of breath, or how about running a race - there are tons of short races that are really fun for participants like the color races or mudders. Studies show that people who have a goal are more successful at sticking with exercise. (WebMD - making goals).