There are many ways to do so, but the best to increase both in the beginning is using the training center for strength and reading books for intelligence.
If your pet's intelligence is really low, the best thing to do is play Mystic Spindles. As you play the game, you earn points that can be spent on int, but the more int your pet has, the more points it costs. So you really want to take advantage of this before reading books.
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