If you are on the hajj journey, before visiting or reaching Medina, the intention must be the first thing to do with. So when you start travel to Madinah, Make niyyah (intention) as such:
 

"O Allah! I start journey to visit the holy tomb of Prophet Muhammad (peace be upon him). Please accept it from me."

While entering the city, enter gently and recite humbly Darud Sharif frequently. So enter at the place i.e. hotel in Madinah near haram or where you are booked according to your hajj package or Umrah package, with same manner.

Put your luggage at your residence, take rest if needed or if you have time, take a shower or perform ablutions i.e. wudu, have a nice and gentle dress, apply perfume and proceed towards the Prophet’s Mosque (Masjid Al Nabvi) while reciting Darud.

Remember, it is not a place like Mecca where there is the house of Allah, but a place of Prophet SAAW where there exists Prophet’s mosque, shrine and the Green Doom. Consequently, the behavior must be organized, humble, calm, mild and gentle with full of respect. The voice must be lower and the steps must be slower.

It is preferred to the mosque through Bab-e-Jibril or Bab-us-Salaam, however, if this is not possible, enter through any other door while reciting Darood Shareef. So where ever you are entering the mosque, enter with your right foot saying,
 

"Allah humma aftah li abwabe rahamte ka"

As it is Sunnah to perform two rakats prayer when entering any mosque, same to the Masjid Al Nabvi applies. Offer two rakahs of nafl as tahiyyat al-masjid (Greeting of the Mosque) in Riaz al-Jannah (Near the tomb of the Prophet) if possible, otherwise anywhere else in the mosque.

That was regarding entering the mosque. View our further articles for more details regarding the procedure to visit Madinah: Saudi Arabia.