Let's go by the film only.

Let's say a timeline like this then:

Summer 1945: Connie's wedding.
Late Summer 1945: Meeting with Sollozzo
December 1945: Vito is shot. Michael saves Vito in the hospital. Paulie is killed.
Very early 1946: Tattaglia's son hit.
Early (January or February) 1946: Michael kills the Turk and Sollozzo; Departs for Sicily.
Spring 1946: Vito comes home from the Hospital. Sometime afterward, Fredo is sent to Nevada.
Summer 1946: Sonny beats Carlo.
1946: Connie's oldest child, Victor, is born (he's referenced by Michael in GF II as being arrested for a petty theft).
Late Summer/Early Fall 1946: Sonny is killed. Appollonia is killed.
Fall 1946: Vito and Barzini arrange the Commission Meeting. Peace is declared.
1947: Vito begins arranging for Michael's return from Sicily.
1949/Early 1950: Michael comes home from Sicily.
Autumn 1950: Michael and Kay meet. They are married not long after.
1951: Anthony is born.
Late 1954/Spring 1955: Vito semi-retires. The meeting with the Capos (where Tessio asks Mike to "take off the handcuffs"). Michael becomes Acting Boss. Tom is demoted from Consligiere; Vito becomes the Unofficial Consigliere of the Family.
1955: Michael Rizzi is born.
Spring/Early Summer 1955: Michael undertakes the trip to Nevada to meet with Moe Greene.
Summer 1955: the scene with Michael and Vito in the Garden.
Late July 1955: Vito's death.
August 1955: The Baptism. Connie, Mama Corleone, Kay and the rest leave for a vacation, which gives Michael the cover to kill Carlo. The assassinations of Barzini, Tattaglia, Stracci, Cuneo, Moe Green, and Carlo.
Late August 1955: The final scenes. The moving trucks are outside the Corleone Compound. With Vito's death and the Massacre of 1955, Michael is officially crowned Boss of the Corleone Family by Neri, Rocco and Clemenza.

(Just my own thoughts here on what happens between I and II in terms of timeline)
Late 1955: The family settles firmly in Lake Tahoe. Michael begins buying up stake in Casinos not long after (unless the Corleone Family already had stakes in the Casinos).
1957: Michael and Hyman Roth enter into business negotiations. Around this time, the Rosato Brothers begin causing trouble. Clemenza dies not long after under mysterious circumstances and Michael appoints Pentangelli as Capo/Unofficial Acting Boss. Willie Cicci becomes Pentangelli's either Top Soldier or Underboss.

April or May 1958: Anthony's communion.

I believe the Corleone Family ran like this, despite the FBI chart; they probably had it a bit wrong:

Michael- Boss
Fredo - "Official" Underboss (but in reality had little power, in essence a Capo with a small crew, running the family's prostitution businesses and clubs)
Pentangelli - Acting Boss (acts as Michael's man on the streets in New York, running the Olive Oil Business and probably responsible for the Family's gambling and policy operations and also getting a taste of the Narcotics trade).
Rocco Lampone- Caporegime/Head of Security (Nevada, reporting to Michael, essentially Michael's muscle)
Al Neri - Caporegime (going between NY and Nevada, reporting to Michael, running the Casinos and other businesses in Nevada, basically acting as an Assassin and as the buffer between New York and Nevada)
Willie Cicci - Caporegime (NY, reporting directly to Pentangelli, probably running the family's gambling and liquor)
Buschetta (aka Michael's Bodyguard)- Chief Enforcer of the Family.

It'd make sense that the guys who were selected to pick off Barzini, Tattagelia, Cuneo, Stracci and Moe Greene got promotions, and I believe Michael's Bodyguard aka Bushchetta (the guy who garrotes Johnny Ola and attempts to kill Roth) is the same guy who killed Moe Greene.