fitness essentials
Credit: Jon Chun

It's Easy and Cost Effective

Getting started with a home gym can be easy and cost effective. With just a little investment you can have a home gym that will help you get started on your fitness goals.  Getting your own equipment is a great cost-effective alternative to joining a gym.  Gyms can be a very significant cost both initially and long term.  Most gym memberships cost between $30-$50 per month, and many make you pay 2 months of dues up front, along with "enrollment fees" that can cost up to $200.   Your initial costs can be $300 or more,  just for signing up!
You can get started on getting fit and reaching your goals at home with much less up front cost.  

Find A Space

Before you start filling your home with equipment, lets scout the space where you plan to spend your time sweating.  I recommend finding a space that is at least 5ft x 5ft and has enough room for you to reach overhead without touching the ceiling.  Is the floor carpeted or hard cement in a garage?  Either way, it would be ideal for you to get a mat to prevent slipping and absorb sweat.
Now that you've got a space to workout in, lets get the tools you'll need.  We're going to start with the most versatile and cost effective equipment.

To Begin - Dumbbells and a Pull-up Bar

The first item on your list should be a good set of dumbbells.  Dumbbells, especially plate loaded ones, are the most versatile exercise tool you can have.  You can press, pull, squat, pickup and swing them in both one and two handed exercise variations.  
Dumbbells come in two varieties: plate loaded and solid.  Plate loaded dumbbells have the best value because you can use one set for a wide variety of weights.  Solid dumbbells are more durable but will cost more to have a variety of weights, and will take up more space.  If you go with solid dumbbells, you should buy one set that you would consider light (you can press them overhead 20+ times, a second you consider heavy (you can press overhead ~5 times), and a third that is somewhere between the first two (you can press it 10-12 times).  
Cap Barbell 40-Pound Dumbbell Set
Amazon Price: $99.99 $49.99 Buy Now
(price as of Jan 9, 2014)

A second essential is a pull-up bar.  A versatile door mounted pull-up bar is very cost effective will allow you to do pull-ups and dips.

Get a Program!

By the time you’ve purchased this equipment, you will still be well below the cost of most memberships, and it will be more than enough equipment to get you in shape effectively.   However, the key to getting the most out of your equipment is to pair it with the a fitness program.  Doing this at home and without supervision and knowledge of exercise programming can be difficult. 
For beginners and people new to exercise the P90X DVDs are great, because they provide guidance, a program, and technique advice.  They can also be a lot of fun.  You won’t need anything more than the equipment listed previously.
P90X2 DVD Workout - Base Kit
Amazon Price: $139.80 Buy Now
(price as of Jan 9, 2014)

If you don't want to invest in buying a program, I would highly recommend seeking out the instruction of someone who understands proper exercise technique and training methods, and can help you build a 3 week plan to get you started.  

Whether you purchase one or get some friendly advice, make sure that you have that program, if you want to keep working out long term. 

That's all you really need to get started.  It's surprisingly simple and really less expensive than investing in a gym membership.   Good luck getting started!