This is an attempt to work out the exact timeline of canon events, since some of them don't have an exact known date of occurrence.

The following happened in this order.

On Halloween night, 1981:

-He went to Peter's hideout and noticed Peter missing and that there was evidence of a struggle (Peter may have been a dunce, but he was able to fool Sirius for long enough to make this happen)
-He went to James and Lily's house, where he found James and Lily dead amidst the rubble of their house
-He gave Harry to Hagrid to take to the Dursleys', per Dumbledore's orders
-He also gave Hagrid his motorbike, since he "wouldn't be needing anymore" (it was kill or be killed, mostly likely kill and then be arrested for what he viewed as a justifiable murder)
-He went looking for Peter.

Then, on November 1st, 1981:

-Somehow there's a delay here and although James and Lily died on Halloween, Harry is not left with the Dursleys until the next night. (At the start of the book, members of the magical community are celebrating Voldemort's defeat [which happened the night before] and then that night is the night that Harry is left with them. This would be the first of November.)

On November 2nd, 1981:

-He tracked Peter down
-Peter accused him of betraying James and Lily
-Peter then caused an explosion, faked his death, and framed Sirius
-Sirius was arrested and sent to Azkaban without a trial

Here's why I think he was arrested after Halloween and not on it: James and Lily died on Halloween night. All of these events taking place on the same night is unlikely. Harry was left on the Dursleys' doorstep in the middle of the night, so Sirius didn't even start looking for Peter until then. The final bit of evidence: there were witnesses who saw Peter accuse Sirius and then frame him. Twelve people died in the explosion, and it's not likely that there would have been twelve people plus witnesses out in the street that late at night.