The Qur'an very emphatically demands that Muslims do NOT befriend non-Muslims. However, in some cases Allah permits his followers to lie and use deception against unbelievers who may think that Muslims are their friends.
Let not the believers take disbelievers for their friends in preference to believers. Whoso doeth that hath no connection with Allah unless (it be) that ye but guard yourselves against them, taking (as it were) security. Allah biddeth you beware (only) of Himself. Unto Allah is the journeying. S. 3:28 Pickthall
Allah is basically telling Muslims that they can pretend to be friends to unbelievers in order to receive their protection, or to protect themselves from them! Here are Ibn Kathir's comments on this verse:
The Prohibition of Supporting the Disbelievers
Allah prohibited His believing servants from becoming supporters of the disbelievers, or to take them as comrades with whom they develop friendships, rather than the believers. Allah warned against such behavior when He said,...
<And whoever does that, will never be helped by Allah in any way> meaning, whoever commits this act that Allah has prohibited, then Allah will discard him. Similarly, Allah said,...
<O you who believe! Take not My enemies and your enemies as friends, showing affection towards them>, until,...
<And whosoever of you does that, then indeed he has gone astray from the straight path.> [60:1]. Allah said,...
<O you who believe! Take not for friends disbelievers instead of believers. Do you wish to offer Allah a manifest proof against yourselves> [4:144], and,...
<O you who believe! Take not the Jews and the Christians as friends, they are but friends of each other. And whoever befriends them, then surely, he is one of them.> [5:51].
Allah said, after mentioning the fact that the faithful believers gave their support to the faithful believers among the Muhajirin, Ansar and Bedouins,...
<And those who disbelieve are allies of one another, (and) if you do not behave the same, there will be Fitnah and oppression on the earth, and a great mischief and corruption.> [8:73].
Allah said next, ...
(unless you indeed fear a danger from them) meaning, except those believers who in some areas or times fear for their safety from the disbelievers. In this case, such believers are allowed to show friendship to the disbelievers OUTWARDLY, but never inwardly. For instance, Al-Bukhari recorded that Abu Ad-Darda' said, "We smile in the face of some people ALTHOUGH OUR HEARTS CURSE THEM.'' Al-Bukhari said that Al-Hasan said, "The TUQYAH is allowed until the Day of Resurrection... (Source; underline and capital emphasis ours)
For the meaning of Tuqyah, or taqiyya, please consult the entry on TAQIYYA.
For a detailed discussion on whether Muslims are allowed befriend non-Muslims, and under what conditions, see the article The Myth of Islamic Tolerance.