Honestly, logging into a novel library has gotten weirdly complicated these days. I've got accounts on like five different apps, and every one of them has a slightly different flow. The core process is usually the same though: you find the login button, which is sometimes hiding under a menu icon or in your profile tab. Then you just enter whatever email or username you signed up with, plus your password. A lot of places now have that 'forgot password' link right there, which is a lifesaver if you're like me and use different passwords for everything. If you signed up with Google or Facebook, look for those little social login icons. Tapping those is usually faster than typing.
Where it gets tricky is when the app is linked to a specific website. Like, I read comics on one platform where my login only works on the mobile version, and I have to use a completely different method on their desktop site. It's a pain. Also, watch out for pop-ups asking if you want to stay logged in. I usually say yes on my personal devices, but if you're sharing a tablet or using a library computer, definitely click 'no' or log out after your session.
One thing I've noticed recently is more platforms asking for two-factor authentication. It's an extra step, typing in a code from your email or an authenticator app, but it does make your account more secure, especially if you've spent money on books or subscriptions. If you're totally stuck, the help or support section on the website or in the app usually has step-by-step guides, sometimes with screenshots. Just search for 'login help' there.