Odysseus safely washed on Ithaca's shore, that's were Athene found him.
When he woke up she introduced herself and disguised him into a old beggar.
When he arrived to his house he saw the mess Penelope hade to deal with. The others hardly noticed him.
Penelope announced that whoever could string Odysseus' bow and shoot an arrow through twelve axes would be hers to marry. They all tried but failed until Odysseus as a "beggar" shot through all twelve and strung the bow.
After making his shot he turned back into normal Odysseus and fought off each suitor one by one. Penelope was in shock on his return.
At first Penelope was scared to think it was Odysseus right away.