None at first. In Amazing #329 Spider-Man undergoes a spontaneous costume transformation when his "Cosmic" powers are revealed to be "Captain Universe" powers.
|New Powers & Abilities:||
A massive increase in his existing powers, including heightened senses and near-indestructibility.
Also: Ability to mentally control his webbing, fire energy bolts, telekinesis, transmutation of matter, and flight.
Spider-Man is initially nervous as he struggles to control his new powers. He later becomes angry and out-of-control.
In Amazing #329 his regains control when he becomes aware of the nature of his powers, and the task which has been entrusted to him.
In that issue, Spider-Man gains basically "all of the powers", but with no explanation.
In the following issues of that arc, Spider-Man discovers new abilities, while increasingly struggling to keep his enhanced powers under control. All this while undergoing attacks by unexpected new foes courtesy of the "Acts of Vengeance" crossover event.
In Amazing Spider-Man (Vol. 1) #329, all is revealed. The "cosmic powers" are actually the powers of Captain Universe, granted by the mysterious Enigma Force.
Go read the issue review for the full story. But the quick version is: "A glitch in the power transfer caused Peter to receive the powers but not the awareness that usually goes with them. He was granted the powers so that he stop the Tri-Sentinel from causing a nuclear explosion that would destroy New York City.
Spidey gains full awareness, along with the costume change. The Tri-Sentinel is defeated, the Captain Universe depart and move on to their next appointment with destiny. Spider-Man is back to "Spider-normal" – and very, very tired.
|Cover Date||Appearance Information|
|Dec 1989||1st: Spectacular Spider-Man (Vol. 1) #158|
|Gains powers. Defeats Trapster.|
|Dec 1989||App: Web of Spider-Man (Vol. 1) #59|
|Dec 1989||App: Amazing Spider-Man (Vol. 1) #327|
|Faces Magneto. Discovers flying ability.|
|Dec 1989||App: Spectacular Spider-Man (Vol. 1) #159|
|Defeats Brothers Grimm. Struggling to control powers.|
|Jan 1990||App: Web of Spider-Man (Vol. 1) #60|
|Jan 1990||App: Amazing Spider-Man (Vol. 1) #328|
|Punches Hulk into orbit.|
|Jan 1990||App: Spectacular Spider-Man (Vol. 1) #160|
|Feb 1990||App: Web of Spider-Man (Vol. 1) #61|
|Defeats Dragon Man.|
|Feb 1990||App: Amazing Spider-Man (Vol. 1) #329|
|Defeats Tri-Sentinel. Saves NYC. Loses cosmic powers.|