The easiest way to get to Istanbul is to take a flight. Pegasus Airlines (You can't see their offers in skyscanner) and Turkish Airlines have regular daily flights to Istanbul. Pegasus generally offers better deals however Turkish Airlines has a wider network. Also, many other airline companies have flights to İstanbul. 

You can also check skyscanner.com or kayak.com​ to find some good deals. An useful tactic is finding the related flight from those search engines and then buying the ticket from the airline website. 

Don't forget Istanbul has two international airports; one on the European side (Atatürk Airport) and the other one is on the Asian side (Sabiha Gokcen Airport). Generally, Turkish Airlines operates at (Atatürk IST Airport) and Pegasus at (Sabiha SAW Airport). 

Additionally, Wizzair offers flights from Budapest to Istanbul.