Variable importance from SVM How to obtain a variable (attribute) importance using SVM? 
 A: Isabelle Guyon, André Elisseeff, "An Introduction to Variable and Feature Selection", JMLR, 3(Mar):1157-1182, 2003. http://jmlr.csail.mit.edu/papers/v3/guyon03a.html
is well worth reading, it will give a good overview of approaches and issues.  The one thing I would add is that feature selection doesn't necessarily improve predictive performance, and can easily make it worse (beacuse it is easy to over-fit the feature selection criterion).  One of the advantages of (especially linear) SVMs is that they work well with large numbers of features (providing you tune the regularisation parameter properly), so there is often no need if you are only interested in prediction.
A: If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See this paper. The (absolute) magnitude of each non-zero weights can give an idea about the importance of the corresponding attribute.
Also look at this paper which uses criteria derived from SVMs to guide the attribute selection.
A: If you use R, the variable importance can be calculated with Importance method in rminer package. This is my sample code:
library(rminer)
M <- fit(y~., data=train, model="svm", kpar=list(sigma=0.10), C=2)
svm.imp <- Importance(M, data=train)

In detail, refer to the following link https://cran.r-project.org/web/packages/rminer/rminer.pdf
