It is not up and running at the moment.
Train on this route was not available till last year however there might be any update.
Apparently the tickets for the new train from Makkah to Madinah will be approx 150 SAR for economy and over 300 SAR for their more luxurious class of travel.
The Madinah Station is approximately 10 km away at best 15-20 minutes drive to Masjid Nabawi. I would say it is in more of a remote location with just a few shops nearby and close to an Al Baik !! I reckon taxi drivers will have more of the upper hand when setting the fare from here
The Harmain Train is not started yet and you need to take taxi or bus from Makkah to Medinah. Private taxi is better but be careful they will ask you more and you have to bargain with them, recently I have travelled from Medinah to Makkah with my parents on a private Toyota Camry for 350 Saudi riyals, It takes about 4 and half hours. If you are alone then in front of Hiton suits and Hyatt Regency Makkah you can get a sharing taxi for 70 riyals. SAPCO VIP bus will charge you 110 riyals.
There are lots of initiatives starting up, spearheaded by the Saudi crown prince, to wean the country off its reliance on petrol. A pleasant byproduct of that could be more trains. So, we may see this elusive Haramain train service quite soon.
InshAllah. Thanks everyone for updating. We will go for the VIP Bus Service better