Understanding Takeout Doubles and the follow-ups is probably more important than any other part of bidding. They come up more often than any convention. This article is meant only as a brief overview and features 4 practice deals at the end. For a full explanation of the subject, please see :"Larry Teaches Doubles."
When your RHO opens the bidding in a suit (on any level), there are two basic kinds of "takeout" double:
1) Opening bid values with the "other 3" suits ("other 3" means at least 3 cards in each other suit)
2) 18+ points of playing strength and any distribution
Here are some examples of #1 when RHO opens 1 :
:
 AQ42
AQ42 3
3 KJ87
KJ87 Q1087
Q1087
,  KJ3
KJ3 65
65 AQ76
AQ76 KJ76
KJ76
, or  AQ42
AQ42 8
8 KJ765
KJ765 K32
K32
.
Here are some examples of #2 when RHO opens 1 :
:
 AKQJ87
AKQJ87 A765
A765 A2
A2 5
5
 ,  AQ4
AQ4 KJ6
KJ6 KQ654
KQ654 A2
A2
,  AK86
AK86 54
54 A
A AKJ765
AKJ765
.
With the examples in #1, the takeout doubler will live with whatever his partner takes out to and not bid again! (Unless, of course, his partner invites by jumping). With the examples in #2, the takeout doubler clearly intends to bid again--whatever his partner does.
The partner of the takeout doubler jumps to invite (9-11) or can make sure of game with more (jump to game or cue-bid). Otherwise, he can bid 1NT (roughly 6-10) or make a minimum suit bid (0-8). For example, after 1 X P, the partner of the doubler bids:
 X P, the partner of the doubler bids:
1 with:
 with:  J654
J654 J765
J765 765
765 J2
J2
, 2 with:
 with:  AQ76
AQ76 A6
A6 10876
10876 432
432
, and 4 with:
 with:  AJ765
AJ765 765
765 AQ2
AQ2 K3
K3
.
Takeout doubles can be made in many situations (such as when the opponents have each bid, or in balancing position). It would take many pages to fully examine this subject, but this article is meant only as a review of the basics.
You might also consider getting Larry's book on Doubles and Redoubles HERE or try Michael's Doubles Webinar which you can find HERE.