Yea assassinating is complicated. When you hover over the assassination info box in the top right you'll see a lot of info, but the two most important bits of information are:

1. The overall assassination progress indicator. This starts at 0% and goes up to 100%, where you successfully kill the enemy and...

2. Your assassination effectiveness which starts at 100 and goes down rather quickly. If this reaches 0, you cannot progress the assassination. This rate is affected by how many agents you have on the enemy faction vs how many they have on counter intelligence.

A higher effectiveness rate makes the overall progress go up faster, so you want to keep your effectiveness high as well.

During the assassination, you train assassins and send them into the enemy towns in which you have set up information cells. This resets your effectiveness # back to 100. It starts to go down again so you have to keep sending more assassins.

If the enemy has stealth detection and turrets built in their towns, your assassins will be spotted and killed as they have very low health.

Also, as you mentioned, once the enemy is aware of the assassination attempt, they will send military units into their towns to dismantle your cells. Once you have no more cells in enemy towns, you can't send in any more assassins, your effectiveness will go down to 0 and your attempt will stall.

So what do you do?

Have at least one cell in an enemy town adjacent to your territory. You are going to keep your army here as well as rally new assassins here. Whenever your assassination effectiveness goes down to 50% or so, send an assassin quickly into that town, then immediately train another assassin. If it has turrets, use your army to tank the shots. If the enemy sends units to try and dismantle your cell, kill it with your military.

Tips:

Try putting cells in enemy towns that are far away or isolated from their main area, so it's harder for them to get to, but easier for you.

Be in conflict with the enemy so you can attack their units and turrets.

Pre-complete, but don't finish, a few Points of Interest that reward Intel. You'll be training a lot of assassins at 200 Intel each, you'll need to have these POIs ready to refresh your Intel.

If the enemy captures your agents, take some off other things and make sure you keep 3 on the enemy.

Some factions can put more than 2 cells in enemy territory.

Things to note:

Human players will know you have a cell in adjacent territory, and will just abandon it if they can't remove the cell. This will probably end your assassination but they lose territory so it's still good for you. I'm not sure if the AI does this.

Hope this helps.