prediction for a linear sum I am learning about SVMs in particular linear SVMs through many questions here. However, one problem i faced is that there seems to be no indepth explanation on how does linear SVM works in terms of predicting new data.

I understand that the main purpose of SVM is to find linear separating hyperplane $w^Tx+b$ and a linear SVM is actually a set of super long equation. 
Let's consider a 2 class problem : A and B. Suppose $(w^*,b^*)$ are the minimizing hyperplane parameters for a fixed choice of $\lambda$.

Then how we classify a new, unlabeled test point $x_{test}$? Simple way that I thought would be reasonable is to have $(w^*)^Tx+b^*&gt;0$ to class A and $(w^*)^Tx+b^*&lt;0$ to class B. But how do we assign if it's 0 and what if there is an outlier in other class for example? IS this a good way of labeling test data?
If it's exactly zero, you might classify it in either class. When using floating point numbers, there's a nearly 0% probability that an observation would ever have a predicted value of exactly zero. There's always some chance that observations will get the wrong label - that's how statistical models work, if you can find some rule that will with 100% certainty give you the right result, you shouldn't be using a statistical model in the first place.

I'm not sure why you want to "label test data". Test data is by definition labeled data that you set apart in order to get a hopefully unbiased evaluation of your model performance. Perhaps you mean making new predictions?