Getting glmnet coefficients at 'best' lambda

Try this:

fit = glmnet(as.matrix(mtcars[-1]), mtcars[,1], 
    lambda=cv.glmnet(as.matrix(mtcars[-1]), mtcars[,1])$lambda.1se)
coef(fit)

Or you can specify a specify a lambda value in coef:

fit = glmnet(as.matrix(mtcars[-1]), mtcars[,1])
coef(fit, s = cv.glmnet(as.matrix(mtcars[-1]), mtcars[,1])$lambda.1se)

You need to pick a "best" lambda, and lambda.1se is a reasonable, or justifiable, one to pick. But you could use cv.glmnet(as.matrix(mtcars[-1]), mtcars[,1])$lambda.min or any other value of lambda that you settle upon as "best" for you.

To extract the optimal lambda, you could type fit$lambda.min

To obtain the coefficients corresponding to the optimal lambda, use coef(fit, s = fit$lambda.min) - please reference p.6 of the Glmnet vignette.

I think the coefficients are produced by a model fitted to the full data, not just testing sets, as mentioned in this page.