Neural Network Timeseries Modeling with Predictor Variables
I think this thesis https://dspace.mit.edu/bitstream/handle/1721.1/99565/924315586-MIT.pdf?sequence=1 is a good starting point for building a model for time series forecasting with so called leading indicators and different machine learning models. Basically you need just to training sets where your inputs are past values of the variable you wish to predict plus the additional indicators (i.e. past_value_t-6, past_value_t-5 ..., past_value_t-1, additional_variable_1, additional_variable_2, ..., additional_variable_n) and the output is either single value in future (t_1) or multiple values (t_1, t_2, ... t_n), in case you wish to predict for example the next twelve moths' sales.

It is also possible to use recursive strategy to generate future values for your prediction variable. In this case you generate next value for the prediction value based on your previous predicted value. However, at least based on my experience the first mentioned direct strategy is way more efficient.