There are few ways. One way is the way you thought about, Yukari makes a gap you go through it and you are in Gensoyko (and will die soon if you are not in the Human village or an other safe place, unless you have a formidable weapon to defend yourself with against hungry youkai.) The second way is the way passing just through the Hakurei Shrine and if you are lucky you get into Gensoyko.
The original script of Dolls is Pseudo Paradise (C62) is a first-hand account of a group of humans who found their way into the border through a gap in a peach tree in a mountain. They all either died or became youkai. According to a chapter in Curiosities of Lotus Asia, Gensoukyou is another layer upon a mountain in a certain district of Japan, where there may be more "natural" gaps, unless they are just left open by Yukari.
Rinnousuke mentions that things that are obsolete objects or things that have gone out of style sort of topple into Gensoukyou in Curiosities of Lotus Asia. From that series it also seems that Yukari travels in and out of the border a lot stealing things, so maybe she "steals" people as well. However Yukari was probably "hibernating" during the events of EoSD when the entire Scarlet Devil Mansion moved into Gensoukyou. So, it is possible that the mansion itself had "gone out of fashion" or Patchouli or Remilia or Sakuya had something to do with moving it there.
In MoF, it seems that Suwako and Kanako volitionally moved to Gensoukyou because they couldn't find enough faith in their native land.
After all, if no one but Yukari could move in and out, and Reimu's job was to protect the border, all she would have to do was keep an eye on Yukari, so I think gaps can happen naturally or without Yukari, she just has the most power over them.