By Car

Udine is on the A23 motorway Udine Tarvisio (Udine nord exit), and on the A4 motorway Venezia-Trieste (Udine sud exit).

By Plane

There are three main airports serving the North-East of Italy:

• Marco Polo Venice International Airport (VCE),
• Canova Treviso International Airport (TSF),
• Trieste Airport (TRS).

From VCE: from the airport, it takes about 20-30 minutes to reach the railway station in Venezia Mestre by bus or taxi (and then about 1 hour 40 minutes to Udine by train). There are two bus services: ATVO Fly Bus (direct connection, recommended), and ACTV (the town public transport service).
ATVO: buses run daily, every 20 minutes approximately, journey time is 20-25 minutes. Tickets cost 8 euro and can be purchased inside the arrival hall at the airport. See here for schedule and online tickets.
ACTV: take the bus number 15, it runs daily, every 30 minutes approximately, journey time is 25-30 minutes. Tickets cost 8 euro and can be purchased inside the arrival hall at the airport. 
Taxi: it takes about 20 minutes from VCE to Venezia Mestre, and it costs about 30 euro.

Once in Venezia Mestre, take a train to Udine. Trains run about every 30 minutes.

A few direct connections from VCE to Udine by bus are also available by FlixBus and BusCenter.

From TSF: from the airport, it takes about 15 minutes to reach Treviso Centrale railway station by bus or taxi, and then about 1 hour 20 minutes to Udine by train.
Take the bus number 6, it runs every 30 minutes and tickets can be bought inside the airport for 1,30 euro.
Once in Treviso Centrale, take a train to Udine. Trains run about every 30 minutes.

From TRS: from the airport, it takes 40 minutes to reach Udine by bus (line number E51). Tickets can be purchased inside the airport, and timetables can be checked here.
The arrival in Udine is at the bus station, about 100 metres from the railway station.

By Train

Udine is on the main line from Venice to Vienna. There are a few direct connections from Rome and Milan to Udine; besides them, getting to Udine by train from almost anywhere else in Italy requires you to change at the Venezia Mestre railway station.

From Vienna, the journey takes between 7 and 9 hours, depending on the chosen train. Check the Austrian railway company OBB for details.

From Trieste, it takes about 1 hour to reach Udine, and trains run about every 30 minutes.

From Venezia Mestre, it takes about 1 hour 40 minutes, and trains run about every 30 minutes. See the Trenitalia railway company for details.