Odo was discovered in 23 58 in an area of space called the Denorios Belt. (A charged plasma field in the Bajoran System). At this time though he was nothing more than a liquid life form. He was taken to Dr Mora Pol at the Bajoran Institute of Science. At this time Bajor was under Cardassian rule so any work carried out by the Institute was to be documented in Cardassian. Odo was labelled and unknown sample, which when translated into Cardassian reads "Odo'ital".
3 days after working with Dr Mora, Odo had doubled in size and learned to mimic 6 simple forms. Dr Mora was still unaware that Odo was a sentient life form though. To communicate this to him one night when the Dr had left Odo transformed himself into a glass beaker that was sitting next to him.
Within 3 or 4 months Odo had grown to a size and skill level to be able to take on humanoid form.
After 7 years as a lab rat Odo left the lab and struck out on his own. Dr Mora didn't believe Odo would be able to fit into any society and would soon return. How wrong he was!
Odo goes to Terok Nor in 2365 at the request/order of Gul Dukat (The current prefect of Bajor) to investigate a murder. In the short time after leaving Dr Mora Odo had gained a reputation as an impartial arbiter by settling simple arguments between Bajorans.
Odo first meets Kira Nerys during this investigation. When she's a suspect. He determines she's innocent and lets her go. Odo fails to find the guilty party but is made a permanent security officer and is ultimately promoted to Chief of Security. Odo's maiden investigation comes unsolved for many years until 2370 when he is forced to re-open the case. Odo discovers that Kira was the killer and Vaatrik (the victim) was a collaborator with a list of other collaborators. With Kira being in the Bajoran resistance it was her job to find the list. And unfortunately Vaatrik discovered her in his shop and she was forced to kill him.
In 2375 10 years after their first meeting Odo finally admits to Kira that he's madly in love with her. He finally does this with the help of one of Dr Bashirs holosuites program characters called Vic Vontaine. Odo and Kira's first kiss is on the Promenade of DS9.
Other significant events in Odo's life:
2367
He's made an officer of the Cardassian court to testify in a case.
2374
Odo along with Kira, Jake Sisko and Rom form a secret resistence cell to
fight the Dominion / Cardassian forces occupying DS9.
2375
Odo goes to Cardassia with Kira and Garek to help the Cardassian Liberation Front, lead by Cardassia's former leader Damar fight against the Dominion.
Odo contracts the virus that's killing the Founders. After Dr Bashir runs tests he discovers that Odo was patient Zero and he has only now shown symptoms. Bashir also finds out that the Virus was created by Section 31