I applied online and got a response about a day or two later to set up a phone screening. The screening took place the day after I responded.
It was more of a phone interview than just a screening, I was asked about 5-7 questions. Questions were about my personal style, my previous job, what I would do in certain situations, and some were just restating a few of the questions I had to answer in my application. At the end of the screening I was asked to come in person for an interview in a few days.
The in person interview was a bit more stressful and professional. The questions here were mostly about previous work experience (Like, I left my previous job without having a new one lined up yet and they wanted to know about that, etc.) and what I know and expect from H&M. They also rehashed a few behavioral questions from my phone interview. I thought that I bombed, but was given a second interview for two days later at the end. Regardless, I recommend doing your research beforehand, I definitely felt like I didn't look into the company enough.
The second interview more or less seems to mean you got the job. It's mostly about what you want from a workplace, how you want to be trained, and what your general working style is. It was more or less just a quick personality rundown to make sure you'll fit in well in a workplace. About twenty minutes in I was given the job and had to fill out some paperwork.
Overall, not to sound cliche, but the best advice I can give really is be yourself and really let your personality shine. You're going to deal with customers all day, so being your brightest during the lengthy interview process goes a long way. Beyond that, do some research and know what to expect, look into H&M's values, and understand some of their policies.