As Will stated you need to work on your whole body not individual parts. Even if you have a chest the size of a 55 gallon barrel you still need to keep working on it.
Specific forearm exercises are the reverse bar-bell curl, forward and reverse wrist curls, and grip strengtheners. Specific Calf exercises are the calf raises, do this both standing and sitting. When doing the sitting calf raises work each leg individually. I've been told that if you want to increase muscle size do 'heavy' weights and low reps (6 - 8) and 3 to 4 sets.
If you are a member of a gym talk to the people who work there, there are also online magazines that can provide guidance. I used Muscle&Fitness to design my new workout. I too am looking to gain size but not specific for the summer. Once I hit the size I want I will change over to strength conditioning. My previous workout was designed by FunkMMA and I did get strong (35lb curls and 470 squats for example) but not much size change.
How much lifting experience do you have? If you are a newbie, stick to the basics. It seems overly simplistic but the big 3 (dead lift, squats, bench press) are a solid base. Not only do they bulk easier than smaller groups, but the first 2 are almost full body exercises, engaging multiple muscles and push your body to produce more testosterone. More testosterone = more full body muscle growth.
After that make sure to cover each muscle group with solid sets, but don't over train and let each muscle group rest. Starting out a 3 day split might be best with something basic like...
Rest 2 days (Light cardio is fine here, but too much will work against your gain goals)
There are a ton of programs, etc but the key is to work out, eat right, get plenty of protein and make sure you are pushing yourself. Newbie gains are the most dramatic, so enjoy them.
They sell hand exercisers for musicians, tennis players and marksmen, I used to keep one in my pocket at all times so that I was squeezing it and working out my grip every day while doing other tasks, do this in addition to pull ups (not girl curl chin ups, they're good for biceps and core but not forearms as much) and some dumb bell workouts and you'll be looking like Popeye in no time. Also stand on the edge of a stair, stand on your tippy toes then lower yourself, these are called calf raises, try to work up to 100 per night.
I always followed the school of thought that you need to develop a strength base first. Do Starting Strength for a while, then switch to a bodybuilding split.
If you want to get bigger and make gains you're going to want to focus on overall strength and compound movements, opposed to putting too much of your focus on forearms and calves or other small muscle groups. There are some good muscle building programs for free on Bodybuilding.com (I personally think the Big Man on Campus workout program is great for beginners). Make sure you are doing plenty of squats, rows, presses, pullups and movements that engage your whole body and core.
Also, diet is just as important, if not more important, when it comes to gaining mass. Rule #1: You're going to need an excess of calories to gain weight. Make sure you're getting good calories though. Things like lean chicken, fish, whole grains, beans,nuts, loads of veggies and fruits are the things you want to load up on throughout the day and avoid any white carbs, sugars, fast foods, etc. Having a protein shake each day will definitely assist in mass gaining as well. Let me know if you need any more advice or tips. Good luck!
Like everyone said - work out your whole body. DO NOT MIRROR MUSCLE! You will look stupid at the beach or pool if your arms are huge and your back and legs are non-existent. Balance is extremely important in body building. Not only because of how you'll look but because of the functionality of your body and the risk for injury is greater when you are not balanced. And remember that your diet is CRITICAL to building your body up. You can spend countless hours at the gym but get no where if you don't have the nutrition to build lean muscle. Protein shakes will be very important but try and get your protein from food like chicken and lean beef too. They are called supplements because they do just that - supplement your diet. And your diet should be a good one.
Here are good resources for you:
You've got about 50 lbs to go before you even think about the term "beefed up." Hit SS for a year, then 5/3/1 with the BBB assistance for a year, eat 5000 calories a day, then cut to 10% BF and you might be somewhere in the neighborhood.
I'm still pretty much a beginner myself too, and I was a rather skinny or wiry type guy before, but in the last four months I gained 20 pounds doing pretty much what all these guys are telling you. Finding out what is a good combination of lifting and resting days for you is important too. For me, I'd do three days of lifting, a rest day, and three more days of lifting.
My schedule looked something like this:
Day 1 - Chest and Triceps
Day 2 - Back and Biceps
Day 3 - Legs and shoulders
I would mix in things like forearms with biceps usually. I eat three times a day as well as having Protein shakes and Nitric Oxide supplements. Look into other supplements that will help with muscle recovery as well.