When coming into Split from the direction of Zagreb on the A1 highway, you will be looking for exit #25.  The signs approaching the exit will say both "Split" and "Dugopolje".  Here is the sign for Split...

and here is the second sign, for Dugopolje.  Both signs are for the same exit.

Here's the next sign for the same exit, mentioning both Split and Dugopolje. 

Here is your exit.  Turn here! 

Immediately after paying your toll (157 kuna from Zagreb; credit cards and euros accepted) you will enter a roundabout. Take the first right out of the roundabout toward Split.

After about 10 minutes (12 km), you will come down out of the mountains and into another roundabout (not shown).  Take the 2nd right, again toward Split.

After about 1 km, take the first exit toward Split.  It looks like this...

 Continue straight (don't turn right) through the first traffic light, here. 

At the next traffic light, shown here, turn right.

 Continue straight, following signs for the ferry port ("Trajektna luka") for about 3.5 km.  Here's the first sign...

...and here is another example of the many that you will see along the way. 

 At about the 3 km point, the left lane will end; stay in the right lane.  It looks like this...

When you reach the city center, the road you are on will curve sharply to the left at the ferry port. 

 You will then see electronic overhead signs, shown below.  Stay right toward Stari Grad / Vis.

 After passing the train and bus stations on the left, the ferry building will be on the right (you will see the sign for Jadrolinija).  Someone from the Croatia team will be waiting for you outside this building.

 When buying your ticket, ask which ferry is for Supetar.  Get in line!

 

 ...and drive onto the boat.

 Exiting the ferry in Supetar, follow the crowd.  You will be forced to go toward the left.

 Continue following this road.  At the beginning you will be on the left side of the road, but you will eventually be forced to cross to the right.

 At the first roundabout, take the second right.  Don't be fooled by the first right, which says Supetar.

 Here's that second exit out of the roundabout...

 After exiting the roundabout, you will see a sign for your next turn. Turn right. 

 And here's what that turn looks like.

You will then follow the road to the large sign for buses and trucks where you will turn right and drive along that road to the hotel.