I'm working on a question in which two explicit knots $K_0,K_1 \subseteq S^3$ are given and the task is to compute the (unsigned) linking number of $L = K_0 \cup K_1$. I'm not really sure how to approach this. I know there's an integral involving the Gauss map that, in theory, can yield the desired number, and there's also a homological approach that I don't really understand.
Question. In general terms, how might one approach a problem such as this?
Addendum. The specific link I'm dealing with is: $$K_0 = \{(e^{i\theta}/\sqrt{2},e^{n i \theta}/\sqrt{2}):\theta \in \mathbb{R}\}, \qquad K_1 = \{(0,e^{i\theta}) : \theta \in \mathbb{R}\}$$
I'm not looking for an answer, but I just wanted a hand getting started. If I'm not mistaken, the linking number should be $n$. To show this, I was thinking of trying to "non-injectively" deform $K_0$ into $$K_0'\{(e^{i\theta},0):\theta \in \mathbb{R}\}$$ in such a way that it ends up looping around $K_0'$ $n$-times. I don't know if this is really the right approach, and if it is I don't know how to get started doing it. In any event, some general advice on how to approach questions of this form would be helpful for me and possibly for others.