As to ideal share :

each co-owner shall have the full ownership of his part and the fruits and benefits pertaining thereto, and he may therefore alienate, assign or mortgage it, and even substitute another person in its enjoyment , except when personal rights are involved.

how co-ownership begin and how it end?

Co-ownership begins at the time when both persons agreed together to own a property in common, full ownership and with ideal share and it will end when the co-owner have its partition over the property or withdraws his right and share being the co-owner.

can the co-owner assign or transfer his right to a third person? can it be done orally?

yes, transfer of right can be done orally, provided that third person agreed and accepts such offer.

In addition, oral agreement is acceptable when the amount of the property does not exceed to P 5,000.00 pesos but beyond that amount written agreement is a must.