Besides offerings, you will get more points with each quest you complete, (there are 4 all together). You'll also get come really cool items, (another even nicer alter, a cloak and a diety stat pet) but the quest line is level dependent so you can't just do them all now (unless you've already power leveled to 80!)
With Tunare as a God, you will need to do a side quest in order to complete the diety quests. The side quest (To Speak As A Dragon) is to learn to speak dragon since the final step of the last quest is to have a chat with Woishi and he doesn't speak common! That quest takes place in Lavastorm and you'll probably need some help to finish it.
Regarding how you can make offerings, it's pretty simple. Drag an item from your inventory to the small icon sized box (labeled "offering") in the lower left hand part of the window that pops up when you click on the alter.
You'll get a message telling you what that item (or stack of items) is worth to your God and if they don't want it, you'll get a message that says "Your God will not be pleased with this offering". If the item is acceptable, it will also light up the radio button in the lower right hand side that is labeled "make offering"
Click that button to complete the transaction!