Ultimately the question is about the causal structure of geometry. The local, causal structure of any event $E$ (represented by a point in Minkowski space) is determined by its light-cone, the boundary between events - past and future - that are spacelike or timelike w.r.t $E$.

In this figure the vertical axis is time (t) and the two horizontal axes are spatial (x,y). The points inside the cone are those which are in the causal past and future of the event $E$. The points lying outside the cone cannot have any causal influence on or cannot be causally affected by $E$. If you pick any point $P =(x,y)$ in this region, then the interval between $E = (0,0)$ and $P$ will be "spacelike". The interval between any two points in Minkowski space is calculated using the (-,+,+) metric:
$$ l_{12}^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2 - c^2(t_1 - t_2)^2 $$
where $c$ is the speed of light. Note the minus sign. That is what distinguishes timelike dimensions from spacelike ones. Points lying on the light-cone itself have zero or "null" separation in this metric.
To answer your question, pick any two points $(x_1,y_1,t_1)$ and $(x_2,y_2,t_2)$ such that $l_{12}^2 \gt 0$. These two points have a space-like separation. As for a concrete example of such a pair of events, consider any two clocks in your house with spatial separation $\delta x$ between them, synchronized to within $\delta t$ seconds of each other such that $\delta x \gt c \delta t$. Then everytime the clocks tick, the separation between those two events in spacelike.
Note: The sign associated with spacelike or timelike intervals is a matter of convention and depends on your choice of metric $(-,+,+)$ or (+,-,-)