Intel recruits on my campus and I applied via the job board of my university. I had to fill out a job application on the Intel website as well as submit my resume and transcript through our Career Services job posting site. It was a bit difficult to deal with the Intel job application site--took more time than I expected it to. I saw that I had been selected to interview on-campus about a week later.
My interview was with a manager and a controller, for 30 minutes each. Both interviews were similar and started off with routine behavioral questions, i.e. "tell me a time you worked in a group." Then I was given scenarios and asked some pretty interesting technical questions, like "If I'm introducing a new product into a market, what do I have to consider in pricing the product?" and questions about fixed and variable costing and product life cycle. Someone I talked to said that they were asked about lease accounting. I've never really had technical questions asked in an interview so it threw me off for a bit at first, but if you paid attention in finance, cost management, and financial accounting classes, it shouldn't be too bad.
The rest of the interview was spent just chatting with the recruiters, both of whom I connected well with. We talked about Intel's new products, Intel's international business, its litigation with AMD and the EU. I didn't have a lot of time to ask questions, but I asked about the intern program. I got the offer call about a week after the on-campus interview.