Becoming thinner is a side effect of eating well and exercise. The common ingredient to all of your effort is YOU and where you want to end up. It's easy to say swimming for an hour burns 510 calories or running an hour burns 560 but individually speaking that's just not the case. Your abilities will vary and the perception of intensity ranges wildly in our minds.
Most of us, if you've been to a hospital and stayed, have observed the "Pain Scale" on the whiteboard nurses use in your room. It contains who your Dr. is, medications you take, upcoming tests, food restrictions and all other basic information about your being there. It's very simplistic and gives the practitioner a general idea of your health when they ask how you're feeling today.
When correlated to your exercise this scale can be used to measure your intensity level no matter what physical endeavor you're doing. Bike, run or swim, the method is not a determining factor but the effort certainly is. If you get to #4 that's a good place to burn fat. Not too tedious and yet not too enjoyable is how it should FEEL.
Don't leave yet, I'm just getting to the science and technology, it's short and sweet. If you're serious about getting in shape I recommend a heart rate monitor. In fact they are so inexpensive these days I think everyone should have one. I'm a Fitbit fan because it can do so much more but basic monitors are cheap to get you started.
What you do need is a basic heart rate knowledge. Start at 220 and subtract your age. This gives you a maximum heart rate. You can use the chart below to see the five ranges of cardiovascular activity. These are generally know as being Resting, Moderate, Fat Burning, Target and Maximum. In essence the most efficient fat burning occurs at 60 to 70% of YOUR maximum. Remember: these are the BASIC guidelines. There are others as your physical ability and cardiovascular progress increases.
Beginning any exercise is a challenge and I recommend asking your Doctor's permission if you're unsure about your capabilities.