The Radar Display on the lower part of your window has a lot of information, once you learn to read it.
The display attempts to show things in 3 dimensions.  Your position is in the center of a ring - as you speed up, the ring gets smaller, meaning that the other objects shown are relatively farther away.  Space stations are shown by their radar symbols - e.g., an 'M' in a box is a mine.  Gates are shown as 'N', 'E', 'W', and 'S'.  Ships are white bars and asteroids are blue squares.
If an object is on your plane, you see only the symbol.  If there's a line extending down from the symbol, the object is below your heading plane, you'll have to nose down to aim to it.
Red objects are Xenon or Enemy ships, with one exception - the mother ship for the race controlling the sector you're in (such as the Teladi Phoenix) is also a red symbol, but it's in a box and it's vertical position trail is not red.  The Xenon ones are.
To head for, say, the North gate using the HUD, swing right or left until the orange 'N' symbol appears dead ahead.  Travel toward the symbol until an up or down line appears; when it does adjust your attitude up or down to make the line go away.  You should be able to see the gate (nearly) dead ahead.
(Tip) When you get a Nav Computer, you'll be able to press the 'N' key and see all of the stations in the sector, plus gates and any Xenon ships, on a two-dimensional grid.  Get this ASAP.
(Tip) The Singularity Accelerator reduces the time it takes to get anywhere by a factor of up to 10.  And it's cheap.