Zagreb to Milan

Basically there is only two ways to get from Zagreb to Italy by rail: either to use direct overnight train #240 Budapest-Venice (departs Zagreb at 23:35 every day, arrival to Venice 7:16 in the morning) + catching Venice-Milan train or go via Ljubljana-Nova Gorica-Gorizia (in this case you will need to go during the day and make at least three changes in order to reach Milan).

For direct overnight train there are special discounted tickets available, start from 15 euro, but you need to purchase them in advance. Full fare on this route is 40 euro, but there is a trick in case you didn't get discounted 15 euro ticket. From the first Slovenian station - Dobova - you can buy ticket to Venice for 25 euro any time. Dobova is only 30 minutes from Zagreb, ticket Zagreb-Dobova cost couple euro.

Route via Nova-Gorica/Gorizia is a little bit more complicated - you'll need to buy international ticket Zagreb-Jesenice (around 16-17 euro), then domestic till Nova Gorica (6 euro), walk/ride a city bus from Nova Gorica train station to Gorizia train station (check google maps). From Gorizia you can already catch domestic Italian trains to Venice.

Venice-Milan: cheapest ticket for regional train cost 14.55 euro (can be bought any time), most expensive ticket for EuroStar train start from 21 euro if bought in advance (while full Eurostar train fare is 30.5 euro). Gorizia-Milan via Venice by regional train will cost a little bit more than 20 euro,