Now that you've got your diet in place and you are comfortable with your new gym, it's time to get a solid workout routine in place. Most guys want to be shaped like a V, myself included. Because of that, I stay away from exercises that require me to bend at the waist like rows and deadlifts. I'm going to mention a bunch of other exercises to do, and you may not be familiar with them. YouTube is your best friend right now. You can find instructional clips showing you how to do just about any exercise. If you can't work out on a workout day, make sure to do something at home, like "burpees," push-ups, and lunges. Saturday and Sunday have been omitted because they are designed to be rest days. Overtraining is just as bad as undertraining. Your body needs rest in order for you to be able to transform it.
Invest in a pull-up bar to use at home until you feel comfortable enough doing pull-ups at the gym. You can probably get a cheap one at Walmart. If you don't already do lots of pull-ups, it may take up to a month before you can do a full set. Also, feel free to take the gym up on that free personal training package.
Here, I outline a workout routine that you can use for the first month of your workout program. Each month, you should attempt to substitute the exercises on this list with others that work that same body parts. In general, chest and arms are on Monday. Tuesday and Thursday are reserved for core muscles and cardio. Wednesday is for shoulders and back and Friday is for arms and legs. Each body is different, though, so you may want to tailor this to your specific case. Feel free to change it however you see fit. The only catch is that you have to stay committed to whatever schedule you ultimately decide to use.

Monday

Stretch
Flat Dumbbell Bench Presses
Incline Barbell Bench Presses
Pushups: 3 Sets To Failure
Incline Dumbbel Fly's
Barbell Curls
Lying Tricep Extensions
Machine Preacher Curls
Tricep Rope Pushdowns
Behind The Back Barbell Wrist Curls

Tuesday

Stretch
Planks: 4 Sets, Holding For 1 Minute Or More
Crunches
Abdominal Wheel Rollouts
Pullovers
Machine Pullovers
Lower Back Hyper-Extensions
High-Intensity, Interval Training ("HIIT")

Wednesday

Stretch
Arnold Presses
Side Dumbbell Raises
Lying Rear Deltoid Raises
Full-Range Lateral Deltoid Raises
Pull-Ups Or Wide-Grip Pull-Downs
Overhand Grip Barbell Rows
Close-Grip Pulldowns

Thursday

Stretch
Planks: 4 Sets, Holding For 1 Minute Or More
Crunches
Abdominal Wheel Rollouts
Pullovers
Machine Pullovers
Lower Back Hyper-Extensions
HIIT

Friday

Stretch
Bench Dips
Preacher Curls
Dumbbell One-Arm Tricep Extensions
Alternate Dumbbell Curl
Full-Range Hamstring Curls
Lying Leg Scissors
Machine Kick-Backs
Squats
Quad Extensions

HIIT

WEEKS 1 AND 2
15 seconds of high-intensity exercise followed by 60 seconds of rest or low-intensity exercise (repeat 10 times)
WEEKS 3 AND 4
30 seconds of high-intensity exercise followed by 60 seconds of rest or low-intensity exercise (repeat 10 times)
WEEKS 5 AND 6
30 seconds: high-intensity exercise followed by 30 seconds of rest or low-intensity exercise (repeat 10 times)
WEEKS 7 AND 8
30 seconds: high-intensity exercise followed by 15 seconds of rest or low-intensity exercise (repeat 25 times)
Working out is a must. Switching up your workout routine is just as important as going to the gym in the first place. For more ideas and tips on this whole process, feel free to check out the following links. They are laden with great information for people looking to take it to the next level.