As far as I recall, there were at least 3 times when they spent time training. - When Vegeta ask Wiss to train him, he spent months traning before Goku's arrival. Later with Goku, they were placed in that strange dimensions where they learnt how to control differently their kis and where they ate all Beerus's pizzas that was hidden in Wiss's staff (so they had to be a while there I guess) , and later they trained in the room of spirit and time for I dont know how many years. You could add Goku's training before fighting Beerus and Freezer I guess. Is there any rough figure you can make from the anime or manga of how many years they were training already?
Before Goku arrived at Beerus' planet, Vegeta has trained for six months under Whis.
It is not cleared whether how long Goku and Vegeta trained together before entering the Hyperbolic Time Chamber. By speculating, they probably spent about 4 months together while Frieza was training.
Well, in the Hyperbolic Time Chamber, they recognize that the place they're in is similar to Kami's Lookout's Hyperbolic Time Chamber but filled with god ki.
We can calculate how long does Goku and Vegeta spent in the Hyperbolic Time Chamber by counting how many pizzas they had eaten.
From the scene where Whis returns all the pizzas from his staff, there are all 10 boxes of pizzas came out of the staff. Let say Goku and Vegeta each ate 1 box of pizza every day, which means in 5 days, they will consumed a total of 10 boxes of pizzas. And now, by calculating the time dilation, spending 5 days in Hyperbolic Time Chamber will make around 20 minutes outside of the chamber. This is quite accurate considering the Z Warriors fighting 1000 Frieza's soldiers, while each person will be fighting around 170 soldiers (or 1 soldier per 7 seconds).
During Universe 6 Saga. they train for three years in the Hyperbolic Time Chamber.
In total, they have trained about 3 years and 10 months together.