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Cardio

Aerobic/cardiovascular exercise, or cardio for short, targets your heart. In addition to improving your heart health, it also provides benefits to many other areas in your body as you'll need to work multiple muscle groups in order to perform aerobic exercise. While the good news is that cardio can be great for your entire body, the bad news is that most people hate doing it because they hate running. It doesn't have to be terrible, however, as there are a couple of variations that might make it easier and more fun for you. There are a few options that can make running easier and more fun, and they only need about 20-30 minutes of your time,  2-3 times per week...

Interval Training

Some find running unappealing because it exhausts your entire body and you have to keep doing it for quite some time. This is because most people train for endurance, but that's not necessary. Interval training is an excellent alternative that essentially involves working much harder for a shorter period of time. (Interval training applies to more than just running, of course, but that's another topic for another time.)

There are several ways of doing interval training but here's one example to give you an idea:
A light jog for a few minutes to get moving (2-5 minutes).
1 minute of high-speed running, then 1 minute of low-speed jogging, repeated 5-10 times (depending on your stamina).
A 5 minute light jog to cool down (or more if necessary).

While you're technically running about as fast as you can for that one minute, you only have to maintain that intensity for a very short period of time. You immediately get a break afterwards. Instead of enduring 30-60 minutes of sustained running, you only have to endure short bursts. For some, this is preferable.

Each burst can vary in timing as well. For example, some structure their intervals like a pyramid, so you start small, peak in the middle of the intervals, and then slow back down towards the end. For some, interval training may sound like complete hell, but if you've never been able to stick to long distance running you may find it easier to accomplish and the results
more quickly rewarding.

Lower Body

With cardio, core, and upper body exercise underway it can sometimes seem a little excessive to work your lower body. In many ways, you will be working muscles that other exercises have already targeted. That said, you'll be neglecting multiple areas if you don't bother with your lower body specifically. Here are a couple of exercises you'll want to do to make sure you're not leaving anything out.
Squats

Squats are a great, simple exercise to strengthen all sorts of good stuff including your legs, lower back, hips, buttocks, and even bones. So long as they're performed correctly, they're an excellent way to target the majority of the muscles in your lower body. So how do you squat correctly?

Stand up straight with your feet firmly planted on the ground approximately shoulder width apart. To help maintain a straight back as you perform the exercise, it's a good idea to focus on an object directly ahead of you at eye level.

2. Contract your abdominal muscles as you bend your legs at the knees. Either stretch your arms out ahead of you, lightly position your hands behind your ears or hold your arms at your side as you slowly lower yourself into a squatting position. Lower your body to a position where your thighs are almost parallel to the floor. Return to the starting position and repeat.

Much like push ups, a squat is a comprehensive exercise that you can do pretty much anywhere. This makes it easy to fit in a set whenever you have some spare time. If you want to make it to 200, the 200 squat program is a good way to get there. If you're looking for something a little less daunting, simply try three sets of 20 squats to start, performing additional squats during the last set if you can manage. Continue to work your way up whenever the exercise gets to be easy. Remember, you won't build additional strength if you don't continue to push yourself as you improve.

"form is vital"

Push ups are a wonderfully effective exercise that work several muscles, including the pectorals, deltoids, and triceps—essentially meaning the muscles in your chest, on the rounded part of your shoulder, and on the backside of your upper arms. While it may seem like a simple exercise to do, good form is vital. this should help you do them correctly:

Lie prone on the ground with hands placed as wide or slightly wider than shoulder width. Keeping the body straight, lower body to the ground by bending arms at the elbows. Raise body up off the ground by extending the arms. Repeat. Body weight should be lifted by the arms; don't be tempted to use your butt, stomach or the lower half of your body to pull yourself up. To maintain correct body alignment, imagine a straight line running from your head down to your ankles. Most 

Push Ups plans which allow you to do the exercise to failure, are a good way to build up your strength quickly, but if you're not quite ready to take on a large goal just use the method described earlier to figure out the right number of push ups per set that works best for you.

mind your body

The Four Core Rules

Before we jump in to the four different types of exercise—cardio, upper body, core, and lower body—and their explanations, here are a few very important rules to remember:

1. Always remember to breathe. This seems obvious, but when you're in the middle of an exercise you may actually forget. In most cases you'll exhale when you do the hard work (e.g. the pushing up part of a push up), and inhale on the easier part (e.g. when you lower your body for the push up). This isn't always the case, however, and special breathing instructions are noted where relevant in this post.
2. Form is extremely important. If you do an exercise wrong, what seems like progress initially will quickly dissipate and possibly result in injury. Be sure you're doing the exercises correctly before you begin. Ask a friend to watch your form first. If you know a professional, ask them to help guide you. While this guide will explain proper form, it is your responsibility to ensure you doing the exercises properly and not cutting any corners.
3. Take it slowly. While aerobic exercise if often the exception, most other exercise is best performed slowly. This doesn't mean you should take long breaks in between each push up and sit up, but that you shouldn't perform each as quickly as possible. Going slowly will work the muscle more and make you stronger.
4. Your goal is to fail. The key to a good work out is failure. That doesn't mean giving up because you're frustrated and tired, but rather pushing the limits of your strength until your strength is spent. Obviously you don't want to push yourself to the point of injury, but that shouldn't be a concern so long as you're exhibiting the proper form. Don't worry too much about the number of repetitions of any given exercise, but instead concentrate on working as hard as you can. A larger number of push ups doesn't necessarily mean you're stronger. Some days you'll have more energy than others and will perform better. Some days you'll perform worse. The key is to do the best you can with all of the energy you have. If you fail, you succeed.