I really like Jaina but she's one of the weaker heroes. When you gain a level with her I highly recommend you get the brilliance aura. It will make Arthas and Jaina even more effective in combat by improving their mana regeneration so they can use more skills. East of where you begin is a small group of ogres which will net you a healing potion which I gave to Jaina. Now take the path north of your starting location and you'll discover a woman with an exclaimation point above her head. She informs you that there is something amiss at the bridge ahead. Head toward the bridge and speak to the man. He gives you the location of another crossing to get across the river. On your way you'll encounter a group of bandits attacking some villagers here. Dispatch them swiftly and you'll receive the optional quest of this chapter:

Optional Quest: Fountain of Health
Not the greatest quest really. It's just a fountain to heal your units (which Arthas is already quite proficient at doing) but nonetheless it may prove useful. On your way to the fountain (it's on the northwest side of the map) try to explore as much of the countryside as possible. There are plenty of monsters here to destroy which can help Jaina gain a couple levels. You will gain a few reinforcements along the way and your footmen will learn the 'defend' skill. It's somewhat useful but only if there are lots of archers. Find the fountain, heal up your units and explore this side of the river.

You'll eventually come across an infected granary - which may indicate the plague could be spreading rapidly - destroy it and continue south. You'll encounter small pockets of undead resistance and eventually a couple of Priests will join you. They can heal your units and will do so automatically if you allow them. Having them near Jaina really helps as she will boost their mana regeneration. Sweet huh? At least it means Arthas can focus on kicking ass. Continue to the west after you've received your next quest: Destroy the grain warehouse. This is the main quest of this chapter. You'll encounter a mortar team which will join you after you eliminate all the undead nearby. Just west of them is a group of enemies guarding a mantle of intelligence +3. I destroyed them and chose to give the mantle to Jaina. She benefits from the intelligence more than Arthas. Now head north and you'll see a cutscene and the warehouse. Destroy the enemies - watch for ghouls ambushing you from the field. Eliminate all resistance and focus your attacks on the warehouse. Mission complete.