Wow. I'm impressed with all of the good advice.
Maybe it has been stated already, but resistance training (weights, body weight exercises), getting those muscles working is one of the most efficient ways to burn fat. It has been shown that a good resistance training session keeps your metabolism up longer than just for the work out duration. This does not mean ignore the importance of cardiovascular training though.
High intensity training is also a great way to pack a good workout into a relatively short period of time. This has also been shown to keep the metabolism up for quite some time after the work out. An example would be: warm up (very important) then sprint, pedal, swim, jump rope all out for 30 seconds then recover (move more slowly to get your heart rate down) for about 90 seconds. Do this eight times in a row. Timing can vary a bit to suit your conditioning (longer sprints, short recovery periods).
Another high intensity exercise method I like is called Tabata (after its originator). Twenty seconds on, ten seconds off eight times for a total of four minutes. Repeat as desired with varied exercises. Four exercises I like to string together this way are: 1) Wall ball; through a medicine ball about eight to ten feet up against a backboard, squat as you're catching it, repeat. 2) Slam ball; throw a non-bouncing heavy ball down to the pavement, follow it down (you'd be in a squat position), stand up lifting the ball overhead and repeat. 3) Box jump; jump onto and off of a box of suitable height (20 seconds jumping, 10 seconds rest). 4) Kettlebell swings (again 20 seconds on ten seconds off for four minutes). I borrowed some of these exercises from friends that to Cross Fit type work outs.
Another toy I like is called the Bulgarian Training Bag. Look it up, it can be used for a lot of exercises and is great for building real core strength.
As stated a number of times by other posters, be safe (don't be causing injury), find things you enjoy doing and will stick with and set goal for, if possible commit to a training partner or personal trainer, and remember - calories out/calories in. If you take in more than you burn, you won't loose weight. You can loose weight eating crap as long as your caloric intake is limited, but it won't be the healthy way to go. It's probably also been stated that if you are putting on some muscle, you may not see your weight drop initially (muscle is more dense than fat) but you will be getting more lean.
I'm 56 and am probably as addicted to exercise (keeps me sane and lets me eat some pizza etc.) as I am knives. I've got a number of joint issues from playing hard all of my life (not so smart days, and/or listening to someone I shouldn't have) so it's a matter of finding variety and what works well for each individual. Really try to come up with a regular time to exercise that is not easily preempted. Knowing that you have a set, uninterpretable time set aside on a regular basis is a big help. Make it a moving meditation if you can. Focus on correct breathing techniques, focus on the muscle groups you're using, focus on correct mechanics. Your workout will be even more rejuvenating and give you a greater since of calm. Of course, if you were a eighteen-year-old with massive amounts of testosterone in your system, you may need to do some head banging first. Though I like music a lot, I can workout fine without it or at least not so loud as to be mind numbing. For the same reason, if I have a work out partner, we don't do a lot of off-the-wall jabbering. One last thing. If you are dealing with injuries/pain/arthritis, it can be helpful to have a trainer that has delt with these things or even see a good physical therapist to get you moving in the right direction. Make sure whomever you see is well qualified, knowledgeable, won't put you through a cookie cutter workout, and has your best interest in mind - it can take some time to find a person you can trust like this. Anyway, hope this helps and I apologize for so much verbiage. Mike