
Commedia dell'arte, an Italian style of comedic and improvisational acting, also influenced Elizabethan theatre - through the use of stock characters, masks, and themes such as adultery and old age.
Professional actors were hired to play for the households of
nobility. The touring companies of these actors eventually replaced
the mystery and morality plays by local actors. In 1572, a law
eliminated the remaining companies lacking formal patronage by
labelling them vagabonds.
It should be noted that all actors were male.
Until the reign of Charles II, female parts were played by
adolescent boy players in women's costume.
The first notable theatre was a building called "the
Theatre" and was developed by James Burbage in
1576. Other new buildings were built soon afterwards: the Curtain
Theatre (1577), the
Rose (1587), the the
Swan (1595), the Globe (1599), the Fortune (1600),
and the Red Bull (1604).
While all these theatres had their distinct characteristics, for
the most part Elizabethan theatres have this common shape: the
public theatres would be three stories high, and built around an
open space at the centre. This open space was usually polygonal in
natural to give an overall rounded effect. The most expensive seats
would be the ones right behind the stage - these were the people
who were there to "see and be seen" by the other audience
members.
The early theatres were vulnerable to fire because they were built
of timber, lath, plaster and thatched roofs. The Globe Theatre, the
famous London theatre where the plays of Shakespeare were performed
starting in 1599, had burned down in 1613. A modern-day
reproduction of the Globe theatre has been built in
England:

Early in 1599, Shakespeare, who had been acting with the Lord Chamberlain's Men since 1594, became a chief shareholder in the company, and by doing so he helped to establish a uniquely successful form of commercial theatre for the actors of his time. This investment gave Shakespeare and the other leading actors both a share in the company's profits and a share in their playhouse. This would explain Shakespeare's capacity to own such a large estate such as New Place!
The below image is a sketch of The Swan Theatre and is what one of
the typical theatres at that time would look like:

References:
Swan Theatre sketch - public domain
Chester mystery plays - image from Book of Days by Robert
Chamber