In the context of support vector regression, the fact that your data is a time series is mainly relevant from a methodological standpoint -- for example, you can't do a k-fold cross validation, and you need to take precautions when running backtests/simulations.
Basically, support vector regression is a discriminative regression technique much like any other discriminative regression technique. You give it a set of input vectors and associated responses, and it fits a model to try and predict the response given a new input vector. Kernel SVR, on the other hand, applies one of many transformations to your data set prior to the learning step. This allows it to pick up nonlinear trends in the data set, unlike e.g. linear regression. A good kernel to start with would probably be the Gaussian RBF -- it will have a hyperparameter you can tune, so try out a couple values. And then when you get a feeling for what's going on you can try out other kernels.
With a time series, an import step is determining what your "feature vector" ${\bf x}$ will be; each $x_i$ is called a "feature" and can be calculated from present or past data, and each $y_i$, the response, will be the future change over some time period of whatever you're trying to predict. Take a stock for example. You have prices over time. Maybe your features are a.) the 200MA-30MA spread and b.) 20-day volatility, so you calculate each ${\bf x_t}$ at each point in time, along with $y_t$, the (say) following week's return on that stock. Thus, your SVR learns how to predict the following week's return based on the present MA spread and 20-day vol. (This strategy won't work, so don't get too excited ;)).
If the papers you read were too difficult, you probably don't want to try to implement an SVM yourself, as it can be complicated. IIRC there is a "kernlab" package for R that has a Kernel SVM implementation with a number of kernels included, so that would provide a quick way to get up and running.
Best Answer
The issue here is that the concept of input and output features don't necessarily exist for time series analysis, at least not in the conventional sense.
For instance, let's say you have features at time t that you are using to predict stock price at time t+1, e.g. price of S&P 500, earnings per share, etc.
To be able to calculate the stock price at time t+1, this necessitates knowing what the values of your explanatory variables are at t + 1 as well.
If you are looking to incorporate the features in forecasting the stock price, then one potential way to do that is by using a standard OLS regression corrected for serial correlation, i.e. correlation between residuals at time t and t+1. By correcting for serial correlation with a suitable remedy (e.g. Cochrane-Orcutt), then this may result in improvements to estimates of stock price with OLS.
However, let us suppose that you wish to use an ML-based model. The first consideration is that the model must be set up to take into account the sequential nature of time series data. For instance, a long-short term memory network (LSTM) is a specialized neural network that is designed for this purpose.
This is an example of electricity consumption prediction with an LSTM, where highly volatile data was modelled using the LSTM with reasonably high standards of accuracy.
In that specific example, x was equal to t-50, with y = t. So, no external predictors were used, rather the time series itself was used as the input and output across different time periods.
Here is a separate example of how LSTM can be run through TensorFlow using R.
A good idea may be to run both instances and compare models. You may find that predicting the time series in its own right without external predictors yields more accurate results.