The way that works best for me is to use time as the extra dimension. Each moment you observe is a 3d “slice” of the universe as you move forward in time at a fixed rate.

To analogize, imagine a circle that lives in an XY plane, moving around in this plane as the plane itself glides along in the Z axis. You’d see some weird snakelike structure growing off towards the sky, but the circle only ever experiences it’s movement in the XY plane. It surely remembers where it was before and has some idea where it will be in 5 minutes, but you can see every point of it’s existence in 3D space all at once. Likewise a 4d being could in principle see your entire timeline at a glance.

This has some weird Lovecraftian implications though if you imagine what that 2d circle would see if it a 3d sphere happened to cross through its plane, and then extrapolate that to the 3d world… The exercise is left to the reader 😉