CURRENT ARTICLE: Lose Weight Lifting Weights
well... the best way to lose fat is to lift weights, eat right, and have a good cardio workout. since you only mentioned the latter, that is what i will focus on.
the fastes way to lose fat is through high intensity interval training (hiit). this is especially popular with people who lift weights as it tends to help them keep muscle better than a slow jog would. in case you are wondering, hiit is where you will do a normal warm up and cool down but for your exercise you will alternate between max intensity and a relatively relaxing recouperating period. so for running, it would be something like jog for 45 seconds and then sprint all out for 15 seconds. when those 15 seconds are over, you shouldn't be able to maintain the same speed anymore and will need to drop down to the slower speed.
hiit is great at losing fat and a few other things, but it doesn't help the heart and lungs in the same way that a 2 or 3 mile run does. so i usually suggest doing the running unless you are very concerned about losing muscle. or the best is that you do some long running and some hiit with your diet and weight programs.