Physically, not hard at all. The border between the three major realms vs the normal world (or “Scientific realm) can be walked across as easily as any state line or map border. Of course, there are defined border crossings and those are secured, and nominally the rest of it is monitored and secured. But as a practical matter, there’s thousands and thousands of miles of border and it is not feasible to have all of it monitored and secured at all times. If you want to slip in without going through a checkpoint, there’s plenty of areas where you might be able to at night if you were diligent. Besides, the worry is more keeping what’s inside from coming out.
As for any legal or passport barriers, as you can’t ride a plane in realm, you would have to get into an area that shares a border. If you’re in the US, you’d have to fly to the Middle East, or Eurozone, or Africa, or Russia. Once there you can move towards the realm easily; there’s also realmwalking travel agencies that can assist with setting you up. There’s reputable agencies, but also there’s that’ll do the Mount Everest thing where they don’t do their due diligence because money spends the same.
If you want to tick all the boxes for legal purposes, the process difficulty varies, depending on your intent, duration of stay, any warning flags you’re giving, and how much cash you’re willing to splash around to make the first three problems go away. One way tickets get more attention than round trips, and such.
As for why you’d go at all, it depends! Assuming you have no relatives there already, Some people want to go big game hunting, some people want to do a pub crawl with Dionysus followers, and a lot of in between. There’s room for actual tourism for assorted reasons, and its safe enough that there’s not TOO much fuss if you’re just making a regular trip, and you follow the instructions of the guides or such, like any trip to a foreign country.
It can, of course, be AMAZINGLY dangerous if you start fucking around and ignoring the experts, but honestly, “Getting killed or fucked up by not following professional advice” is pretty easy in the real world! The number of people who’ve had Bad Experiences in Yellowstone National Park just by wandering around after dark, off the trails, or ignoring warning signs is a good example. Same general idea though the ‘danger areas’ are a little broader than random pools of boiling water.
To borrow the US system, realm border areas are Class 1 or Class 2 travel advisory. The realms themselves inside are mostly Class 2, but there’s areas that will be Class 3; these tend to fluctuate with the political situation. Class 4 happens on occasion but it’s relatively rare, and once an area is under Class 3, there’s risk premium for hiring people, and a lot of groups just won’t do Class 4 areas with tourists at all because it’s not worth it.