We typically have a separate session just for level up or sometimes at the start of end of an otherwise shorter session.
Our group only levels during downtime as we require training, research, etc. + experience (we don't track XP explicitly) to gain levels. To gain a level you need to spend 1 week of downtime and 10 GP* per level. So to get to 15th level (our current level) the Wizard had to conduct research and experiments for 15 weeks** and spend 150 GP to get from 14th to 15th level, after they have gained enough field experience (XP). So we tend to spend a whole session doing downtime activities and a portion of this is training to get to the next level.
* we use a silver standard
** A week is spending approximately 40+ hours performing the required activity. If you one spend 20 hrs, then you only get the benefit of 1/2 week.