In my Moms day (when she was cloth diapering my siblings and I), cloth diapers did up with diaper pins. They were cute, useful after diapering days were done and they leave a lot of sposie parents worried that if they were to try cloth they would prick their baby.
Today the majority of cloth diapers do up very much like disposable diapers. All the various forms of fitted's (fitted, AIO, AI2, pocket) do up either with Velcro (aplix), or snaps. And prefolds are usually done up with snappi's (or similar product), or held closed by the diaper cover.
Velcro is a popular and easy choice. It has a reputation for being the easiest way to close something up. Children's running shoes being a great example of this reputation. For Moms sewing their own diapers Velcro is also an easy choice. My mom even added to my prefolds for my toy dolls, likewise I have added it to my prefold hybrids. If baby has older siblings who will also be helping with diaper changes, they will find the Velcro an easy choice to learn too (my 3rd child loves babies and learned to change baby #5 in fitted Velcro diapers at age 7 - her choice, she really wanted to, now 13 she says he was like having the best doll ever). The down fall of velcro is that it can get worn out over time. Take care of your Velcro doing it up before laundering. This prolongs it's life. On the plus side if the Velcro on your diaper is wearing out you can easily replace it yourself.
The other popular choice for the various forms if fitted diapers is snaps. These are also an easy choice (not as easy as Velcro, especially for young helpful siblings but still easy). One of the benefits of snaps is that with multiple snaps placed on a diaper you have great variety in sizing (smaller, bigger, looser it tighter). For moms sewing thier own diapers these are easily available in fabric stores and come in a multitude of colours. On the downside they do not handle very high heat well as they are plastic, check manufacturer's instructions before laundry time, and ask other cloth moms.
Prefolds and flats dont usually have snaps and Velcro, but they also dont usually have pins anymore either. The most common way to do up flats and prefolds is with a snappi. A snappi has 3 points in which it hooks into the cloth of the diaper and holds it all in. They are also very inexpensive and you only need a few - unless you loose small items due to misplacing, which in my house happens often. We find things in the oddest of places lol.