Moving from the 1st stage of the labour, into the 2nd stage of the labour, can be detected by your caregiver either visually or by doing a vaginal examination. If you do not have an epidural in place, then the midwife with you will probably recognise the change by the way that you grunt, moan or push, and possibly with a trickle of bright blood coming away from the vagina. It is not essential that you have a vaginal examination to confirm that the cervix is fully dilated, unless the midwife is concerned there might be problems. If you have an epidural in place, then a vaginal examination will usually need to be done to confirm that you are indeed fully dilated, as you will not always display the typical signs of the 2nd stage.
If you have a private obstetrician, they will usually keep in regular phone contact with the midwife, but not be present until you are well into the active pushing phase, and the baby's head is well down, or can be seen (unless they are needed earlier due to complications). If your doctor is trying to organise their other commitments, they may ask the midwife to perform vaginal examinations more frequently, so that they have a better idea of 'where you are up to'.
Sometimes the pushing stage is unexpected. If you are progressing faster than normal, your announcement of "I want to push" may be received by your caregiver with some scepticism (or even disbelief). If this is the case, trust your instincts (they are usually right) and ask the midwife to check your dilation, so that she can be prepared for the birth!
NOTE: The following information is based on what to expect in an Australian context. If you live in another country the procedures may be different.