You really need to include some resistance training, it is as important as cardio.
The best way is with free weights but if not then body weight exercises are excellent, or you can use machines. The reason free weights/body weight are better is that they usually use more muscle groups at the same time (rather than isolating a particular muscle) and the movements are functional, in that they often mimic the actions you undertake in day to day life so make you better prepared for that and less likely to injure yourself doing something like lifting.
The best way to start is to get a personal trainer for one or two sessions if you can possibly afford it. They can show you a good set of basic exercises, show you correct technique and help make sure you are doing exercises appropriate for you. Failing that, a gym instructor/assistant should help you if it is a decent gym. You can also check good exercises and technique on YouTube.
As a start I would recommend a routine to include 2-3 sets of push ups, squats, lunges, (add weight to last two as and when you can do them easily), tricep dips (or kickbacks with weights), bench press, shoulder press, supermans, planks and side planks. This will give you a great all over workout and should take maybe 1/2 an hour. Then interval train on your choice of cardio machine for 12-20 minutes, rather than working steadily. Follow with a good stretch 
. I promise you will see an amazing difference in your body and fitness level within a month, max.