Sauron was Morgoth's servant and pursued his ends while Morgoth was unable to. What level of autonomy was he granted to do this?
In the Silmarillion, Sauron is referred to as a "lieutenant of Melkor" (Silmarillion. ch.3) and was given charge of Angband, a fortress and armory that Melkor had made. This seems to me to imply that Sauron worked directly under Melkor as a military commander. This is strengthened by this quote, from Chapter 17
But it was said afterwards among the Eldar that when Men awoke in Hildórien at the rising of the Sun the spies of Morgoth were watchful, and tidings were soon brought to him; and this seemed to him so great a matter that secretly under shadow he himself departed from Angband, and went forth into Middle-earth, leaving to Sauron the command of the War.
On the one hand, Sauron is a trusted enough lieutenant to be given complete control of the war in Beleriand. However, this also implies that his goals are totally aligned with Melkor's at this point, and that he isn't really a free agent with his own agenda.
Later on, in Chapter 18:
[Sauron] took Minas Ithil by assault, for a dark cloud of fear fell upon those that defended it; and Orodreth was driven out, and fled to Nargothrond. Then Sauron made it into a watchtower for Morgoth.
Again, his actions are ever in the service of Melkor. As an aside, it seems that places named Minas Tirith have followed him around. After he took Minas Ithil in the third age, Minas Anor was renamed Minas Tirith ("Tower of Guard") too. I wonder if he felt the irony.
After Melkor's fall and the end of the first age, of course, Sauron was a completely free agent, for the very first time. We know how that worked out for him in the end.