Reducing TSP to HAM-CYCLE to VERTEX-COVER to CLIQUE to 3 CNF-SAT to SAT
A couple of the ones you're looking at here are pretty simple actually (at least to sketch!). For all of these, there are many other ways to do it, even many other sensible ways, so these are just attempts to pick the simpler approaches (we'll see if I succeed).

As mentioned in one of the comments on the question, $3SAT$ to $SAT$ is trivial, an instance of $3SAT$ is already and instance of $SAT$, so there's no work needed at all. 

To get from $VERTEX$ $COVER$ $(VC)$ to $CLIQUE$ we can do a couple of short jumps, that'll also put another problem in the loop. $VC$ is the dual of $INDEPENDENT$ $SET$ $(IS)$, that is, we can find a vertex cover of size $k$ in a graph $G$ iff we can find an independent set of size $n-k$ in $G$. Play around with this a little and you'll see why this is true. If we then take the edge-complement graph $\bar{G}$ of $G$, an independent set of size $t$ in $G$ is the same as a clique of size $t$ in $\bar{G}$, so that gets us to $CLIQUE$.