Do the actors really go nude in the shooting of the movies?

That's really up to the actor (if they have enough clout).

Very often it is written into contracts whether an actor will go fully or partially nude, regardless of whether their on screen character does so.

During filming it is not unknown for filmmakers to use body doubles for close up shots, and many times during mid to long shots an actor might request to wear skin tone pieces which cover their genitals or nipples.

*As an example - here is Megan Fox (who will not do fully nude roles) wearing flesh-colored nipple covers and 'briefs' for a supposedly nude swimming shot in the film Jennifer's Body.*

From the article The Naked Truth about on-screen nudity

The subject of nudity clauses has come up with increasing regularity these days, particularly as more flesh is being revealed on network television. Though naked actors may be more prevalent than ever, the choice not to show all is also more accepted.

Megan Fox, Jessica Alba, Scarlett Johansson – who have gone on record as refusing to do full nudity.

[...]

Given the strict union guidelines around on-set nudity, there’s seldom a reason for performers to be surprised. Actors must be told of any nude scenes well in advance and nudity waivers require directors to itemize exactly what will be shown and how.

[...]

As Anne Hathaway told National Public Radio, the typical process goes like this:

• “The director submits a shot list, and you look over them for approval. And a lot of times, if an actor feels the shot demands a lot of them, they'll demand money for it.”

... for the 2010 film, Love and Other Drugs, she and Jake Gyllenhaal agreed to waive the nudity clause, allowing director Edward Zwick to shoot what he wanted. But she and Gyllenhaal had final cut over those scenes, which she exercised, asking for about five seconds of the film to be cut...

From the article Fakin' It - Actors discuss the ins and outs of making a successful sex scene:

While women wear body stockings, G-strings, and pasties on-set, men get what is known as a 'sock':

• "It's a flesh-colored pouch that wraps your genitals up like a bag of leprechaun's gold."

There is also the option of body doubles:

• 9 Famous Nude Scenes That Used Body Doubles
• Stars who used nude body doubles

There are a variety of techniques that directors can employ, depending on their and the actor's preferences (depending on how much the actor is worth, low grade actors would not get a choice):

• The easiest is for the actor to be nude and for editing to ensure that the finished film is decent and their modesty is protected. However many very famous actors refuse this as they know that the prints of them naked will almost definitely find their way out of the studio and onto the internet.

• The actor can wear clothes and these can be kept out of shot with good editing.

• The actor can wear special body suits (these appearing often in the background of things like 'Rome') which makes it look like they are naked when they are actually not.

• The actor's face is used for some close up shots and a body double is used for the rest of the scene ('Love Actually' shows some body doubles at work).

• Now, I suppose CGI could be employed too.

• Also, I think that there is a technique used where the actor is clothed but the script refers to them as being naked. This seemed to be what they did in Friends once when Chandler was handcuffed in Rachel's boss's office. Chandler was wearing his shirt, boxer shorts and socks but Rachel and the other seemed to be discussing the situation as if he was naked (ISTR Rachel was discussing the size of his manhood and made a deal where she agreed to exaggerate it).