The Takeout Double shows at least 3 cards in all unbid suits if only 12-17 points (with extreme shape, such as 4-4-4-1 or 4-4-5-0 you might make a takeout double with 11 HCP).  If you have at least 18 points you must double first and can have any shape.
The typical interpretation of a takeout double is "Partner, please pick an unbid suit."
The doubler must be ready to play in just about any suit the responder may pick (with the exception of the strong double).

The answer is because we have three suits of similar length and we would like to ask partner to choose the one with which she has the best fit. It is our only way to get into the bidding because we do not hold a five-card major to bid because without five cards in a suit we cannot make an overcall, and therefore would be unable to make a call without the help of a Takeout Double.

- (0 to 8) total points - Bid 4-card major.  If no major bid longest minor at the cheapest level.
- (9 to 11) total points - jump one level into your major or longest minor.
- (12+ ) total points - jump to game if you know you have a fit or cuebid (bidding the opponent suit) to ascertain the best strain.

Bidding 1NT (6-9) points and a stopper in opponent's bid suit
Bidding 2NT (10-12) and a stopper in opponent's bid suit
Bidding 3NT (13+) and a stopper in opponent's bid suit

Often times the opponents do not oblige us by passing when we enter the auction with a takeout double.  However, this is not all bad.  When RHO bids, we are off the hook.  We can pass if we have very few points.  
If RHO bids, we also have the additional option here of doubling.  A double in this situation is called a “responsive double”.  The double says I have enough points to respond to you, but I do not know where to play this hand (I don’t have a 5-card suit).  For example, the auction precedes 1♦ - X - 1♠ - ? and you hold:
♠Kx, ♥Axxx, ♦xxxx, ♣Jxx
Partner’s takeout double showed 12+ HCP points.  You have 8 HCP.  So you have at least as many HCP as the opponent’s.  So there is no reason not to compete for the right to declare this contract.  However, you have no idea where to play this contract.  NT, hearts, or even clubs might be right.  So you double.  The double here is “responsive”.  It says that you have enough points to compete but don’t know where to play it.  Partner will assume you have no 5-card suit, because you didn’t bid it.
Since we could pass with very few points, and we could double with points and no 5-card suit, a “free bid” here shows some points and a 5-card suit. Here are the levels:
1) Pass 0-5
2) The minimum bid shows 6-9 points.
3) A jump shows 10-12 points.
4) A jump to game shows 13-15 points.  
5) A cue bid is game forcing (when you not sure where do you want to play) ;
6) 1NT shows 7-10 with at least diamonds stopped.  Partner implied something in spades;
7) 2NT shows 11-12 with at least diamonds stopped.  Partner implied something in spades; and
8) 3NT shows 13-15 with both diamonds and spades stopped.  You can cue bid if you are missing the other stopper.

After partner bids a suit:
1) A raise of partner’s suit to game is to play since partner limited her hand;
2) A jump raise is invitational to game; and
3) A single raise doesn’t usually show any extra values but is just confirming a fit.  
For example: 1♦ - X – P – 1♠
                        P - ?
1) 2♠ = 4 spades and not enough for game opposite 0-8;
2) 3♠ = 4 spades and 18 or 19 points (inviting game opposite 6-8 points);
3) 4♠ = 4 spades and 23+ points; and
4) 2♦ followed by 3♠ shows 20-22 points with spade support.

If you double and then bid your own suit, you are showing 5+ cards in that suit and a hand that was too strong to overcall.  Remember you can overcall with as much as 17 HCP.  So, doubling and then bidding your own suit shows 18+ points.  
You bid is forcing for one round.  Partner know that you have a big hand, because if you had a minimum, you would pass since you told partner to pick her best suit and she did.  For example:
1S - X – P - 2D
 P -  2♥ (shows 18+ points and is forcing for 1 round)