How do you obtain recruit heroes tickets?

You will get a few free tickets every day to use (although only on that day) and you can buy more if you want but the game also gives out tickets as rewards.

Complete the daily tasks each day in the Quest list and you will get 3 normal blue tickets at 260 points, and 1 purple advanced ticket at 500 points.

Reach the third reward box in the Clash of provinces event when it is active and you will get 1 Orange super ticket (2 if you complete the zone commemoration research). If your province wins the CoP event then your rewards will also include purple or orange tickets if your castle level is high enough.

There are also other events that can offer tickets rewards, for example the recent Christmas event had many ways to get them. The Reign of chaos event can give you special seasonal tickets at the end if you do well.