With pen and paper everything is easy to check. You look into the ballot before it is sealed, you check if everyone just throws in one ballot, and on the end you can count the ballots easily. This is something which can be checked trivially.
It is also something that can be manipulated easily.
The usual way is to replace entire ballot boxes with ones filled with the desired votes. It's unknown how much this has been used but around the so-called democratic world full ballot boxes have been found at landfills etc. and the best case scenario has them simply being misplaced and not counted, and the worst case scenario is that the votes were replaced. As it doesn't make sense to drop full ballot boxes at landfills (they are usually reused multiple times, and of course always emptied), the worst case scenario must be the reason.
Some countries seal the boxes and check the seal before opening the boxes and allowing the votes inside to be counted. Sounds secure until you learn that the ballot boxes are only sealed as they leave the polling stations. Until then the full ones are stored in a locked room as empty ones are switched in to allow room for more votes. This locked room is usually just any available store room at the polling location which means that the regular janitor and some staff would have the key. It would not be hard to bribe someone for a copy of the key and then it's just a matter of doing the switch.
In other types of 'democracies' you push people to vote a certain way. Just like in old Iraq where Saddam Hussein in the last election went from 98% of the votes to 100%. It was an open and free election but the other candidates simply either didn't get any votes or had accidents just before the election and had to retire. Also the ballots with votes for other candidates were examined for fingerprints etc. and the voter usually then got a visit from the secret police that wanted to know why they didn't vote for Saddam. Most people then said it was an accident and after having promised to vote for Saddam the next time, they were let off with a warning. If they didn't... Well, let's just say they didn't get to vote in the next election.