As a rule of thumb I always look at the motor plate. This will be marked up with the motor voltage, current and importantly connection details.
Usually motors in the UK above 4kw are designed to be delta connected when up and running. Although if you have a word with your re-wind people they will wind your motor anyway you want. Star or Delta run.
I like to say that the motor when connected in star is two windings in series therefore less power, and when in delta the motor windings are individually connected across the supply therefore more power.
When explaining too younger sparks, if you imagine a (6 connection A1,A2 B1,B2 C1,C2) star connected motor with the links on for star. Then the motor connected with the links in delta(6 connection A1,A2 B1,B2 C1,C2). With these two in mind.....
When running a motor on star-delta all you are doing with your external contactors is moving the links outside the motor and into your panel. Hence no links required on the motor terminals. Star for running up, delta for running.
Star-delta is not always necessary, if you are lucky enough to visit a power station or an Aluminum smelting works (somewhere that generates there own electric), they just start their motors direct on line. With no current limitations you can do this. Watch those lights dim though!
However where I used to work, if you started the two main motors both at the same time it used to take the main incomer out. Not good.
I have seen rotor resistance starters, rotor regulator starters, vapourmatic starters, liquid starter starters, soft starters and VSD's all which are common where I work now.
All of which gives you a good grounding in motor starters.