An exercise routine for fat loss has two components - the weightlifting component, which will help you maintain your lean body mass, and the cardio component, which will help you burn more calories to lose fat faster.
The following programs are intended for beginners to weightlifting or people who have had a long break from the gym. The beginner program should be used for at least 6 months. After 3 months, you may switch to a different beginner program if you wish. I suggest advancing to an intermediate level program after completing the beginner program.
The weightlifting notation I will be using looks like: Squats 3x6-10. This means you should do 3 sets of 6-10 reps with 45 seconds to 1.5 minutes between sets. If you are learning a new exercise, remember to start with light weights and be extra cautious to have correct form. If you are unsure about correct form, seek the aide of a personal trainer.
Read about sets, reps, specific warmups, and HIIT here. Review and learn how to do exercises by looking at exercise demonstrations.
Remember to increase your weights if you can complete the reps easily (and with proper form). Your last two reps should feel fairly hard, and you should not be able to complete more than 1 extra rep (ie. near failure). Also, when your rep range is decreased (eg. from 8-12 to 6-10) you will want to increase the weight slightly.