TL;DR You basically can't guarantee a villager of choice will want to move out. You can manipulate things slightly, but it's still mostly chance and random numbers. You can tweak the chances a little by lowering an unwanted villagers friendship with you from 25 down to 0, while increasing friendship with other villagers as much as possible. Increasing friendship with other villagers is more likely to be productive than bullying the one villager you don't like.
Here's a Twitter thread by Ninjii, who datamines the game and from my experience, is usually correct. As it explains:
you must have at least 6 villagers living on your island before any will consider moving out
on a given day, the % chance of somebody asking to move is given by (v * 5) + c, where v is the amount of villagers you have, and c is the 'MoveOutTalkCount', the amount of days since you last told a villager to leave or stay (maxing at 30)
there is a 5-day cooldown after telling a villager to leave or stay - so nobody will ask to move if MoveOutTalkCount <= 5
there is a 15-day cooldown starting on the day the villager has left the island and freed up the plot (this is called the 'MoveOutSkipCount')
if these checks pass, a random villager will be picked who will ask to move out
each villager's chance is based on friendship and calculated by floor((300 - a) / 10) - r
floor means rouding down to a whole number
a = average friendship they have with all island residents
r = amount of residents with >200 friendship
friendship is 0-255 (starting at 25), so this chance starts at 27 for new villagers, going down with higher friendship levels
villagers will be excluded if:
- their house is being moved
- their birthday was in the last 7 days
- they were picked last time and told to stay
- they moved in most recently
The thread goes onto explain that Ninjii isn't sure about the birthday rule, and that it might also be a case of 'coming up in 7 days' instead of 'being in the last 7 days', but there isn't any more information on that. Note that the 'residents' in the values for 'a' and 'r' are player characters, not other npc's on your island. So, if you share your game and island with another person, your friendship + their friendship with the villager is averaged.
Fredy31's answer is correct in stating that talking with Isabelle doesn't do anything to make villagers move out. That functionality seems to exist only to handle potentially offensive clothes or catchphrases that could be introduced through multiplayer.
But hitting with a net could do something. Like the above quoted Twitter thread says, villagers start with a friendship rate of 25, and this can be brought down to 0. Pushing a villager or hitting with a net, if done right, can earn you a -3 point decrease. This image from the animal crossing fandom wiki explains: Pushing a villager or hitting them with a net until they get upset decreases friendship points by 3. But when the villager gets upset, there's a 20 percent change you can earn the points back by apologizing, and if the villager is happy with your apology, you can even increase friendship by 3 points. This is fickle, but bullying is the only way to decrease your friendship points with a villager to 0.
Another way to decrease your personal friendship points would be to gift your unwanted villager garbage or spoiled turnips, which will give you a -2 point decrease until you reach friendship levels where you can't gift anything.
Fencing a villager off from the rest of the island is useless, villagers can teleport and your fences will be useless. It does nothing to lower your friendship with one villager or increasing friendship with others, and thus does nothing to increase chances of villagers moving out.
Like Ninjii said on Twitter, the 'base' chance of a villager moving out is 27. You can increase this to a maximum 'chance' of 30, when their friendship points with you are at 0. On the other hand, increasing friendship levels to e.g. 201 points will give you a 'chance' of that villager moving out of 8. In the end, the game sums the chances (calculated by floor((300 - a) / 10) - r) for each villager, generates a random number between 0 and the total, and then looks at where it falls to determine who gets picked.
So lowering friendship with 1 villager while maxing out all others gives you a larger range of random numbers for the low friendship villager to be randomly picked, while lowering the ranges of all other numbers. But increasing friendship with others (and so decreasing their chance of being picked to move out) seems to be more productive than aiming for those extra 3 chance points you get for decreasing friendship with your hated villager.
After you've manipulated friendship levels, you can apply one other trick to speed things up: You can avoid the 5 day cool-down after telling a villager to leave or stay by either not starting the conversation (if a wrong villager has the cloud above their heads that may suggest leaving), or by resetting the game (close software and restart) before telling the villager to leave or stay. If you do so, on the next day, the game will again use the (v*5)+c calculation to calculate whether a villager will be leaving.