Time series analysis for 2 series where one is dependent on another If I have two time series $A$ and $B$.
$A$ is dependent on $B$.
I want to forecast future values of $B$.
What statistical techniques should I learn and try?
As an example consider a time series of sales of Apple ipods every month.
Another time series is the number of defects in ipods reported.
Clearly if the sales are more the defects will be more too, assuming a constant
probability for a defect to occur.
How to use both $A$ and $B$ to forecast $B$?
 A: You should learn and try time series forecasting with leading indicator The easiest way to start is perhaps to replicate the example in Box and Jenkings book, mentioned in the link as the source of the data. If you need a good reference for formal writings, check out this one.
Note that when your purpose is forecasting you just don't care about causation. There are two different worlds. If you want to learn more on this, read Galit Shmueli's To Explain or To Predict? in Statistical Science. I do not know how that comment on causation adds to your question, which is in my view neither too broad nor unclear. I can even upvote it as a good question.
A: You are looking for Vector Autoregression (VAR), which should be discussed in any good econometrics textbook. Good luck!
A: It all depends on your goal. Do you want to forecast sales based on defects or Do you want to capture the relationship between sales and defects
If you want both 
There are two options . You can run a simple linear regression A = (Beta0)+ (alpha)*B , without bothering about the time series properties of the series. 
The better option is to use VAR (Vector Autoregression models) followed by Granger causality to understand which series is affecting which and if the effect is instantaneous or the lagged values also come into play.
If your only aim is forecasting , you can also look into neural networks for time series, neural networks dont give you the relationship between the series, but sometime outperform the statistical models in terms of forecasting. 
A: here is basically the model you're looking. 
\begin{equation}
x_{j,t} = \sum_{l=1}^n \sum_{k=1}^{K} A_{i,k}x_{k, t-l}
\end{equation}
In this equation you write the random variable $x_j$ at time t being linearly dependent on observed value of all $K$ random variables in the past $n$ previous time steps. In a more compact matrix notation, the above equation looks like this:
\begin{equation}
X = AT
\end{equation}
where matrix $T$ is a $K\times n$ matrix of your past observations for the $K$ variables. Using this, it's obvious to see the maximum likelihood estimate for your interaction matrix $A$ is:
\begin{equation}
A_{MLE} = X \, T^{t} \, (T T^{t})^{-1}
\end{equation}
