Bismillah.
Allah (SWT) begins describing the 3rd group of people, the hypocrites, in these ayat. Hypocrites are those people who have one thing in their heart and show another thing in their actions. They are different than what they publicize. These people will be in the lowest pit of the Hellfire in the Akhirah.
And of the people are some who say, “We believe in Allāh and the Last Day,” but they are not believers.
The first quality Allah (SWT) mentions is that they say with their tongues that they are believers when they truly are not. They do not prove their belief through their actions. They say one thing, but do something else. They call themselves Muslims, but are nowhere near to fulfill the commands of Allah (SWT). It’s not enough for us to call ourselves by Muslim names such as Abdullah or Maryam or Muhammad thinking our label is sufficient. We need to prove through our actions that we truly are Muslims.
They [think to] deceive Allāh and those who believe, but they deceive not except themselves and perceive [it] not.
What do they think, they are deceiving Allah (SWT)? Do they think that Allah (SWT) does not know? Do they think they can get away with all this? They are not deceiving anyone except themselves. They are not harming anyone except themselves, if only they knew. Do you think when you hide all these secrets in your heart that no one knows? Do you think you’re getting away with everything? How will you get away from Allah (SWT) on the Day of Judgment? How will you hide your sins then? You’re not hurting Allah (SWT) with this deception, you are only deceiving yourself and hurting yourself. 
In their hearts is disease, so Allāh has increased their disease; and for them is a painful punishment because they [habitually] used to lie.
They have a disease in their heart, the disease of hypocrisy and doubt. They live an uneasy life always confused and lost. But the punishment will not end when they die, it will go on with a painful punishment in the Hereafter. They receive such a great punishment because they used to lie. They lied to others and to themselves thinking they got away with all their white and black lies. Well Allah (SWT) has news for you, you got away with nothing. Instead, the cause of your destruction is your lying habit. 
And when it is said to them, “Do not cause corruption on the earth,” they say, “We are but reformers.”
When you talk to these people and you tell them not to create problems on the earth, they say we are only doing good. When they cause fights and spread gossip and lies, they try to justify their actions saying they are only trying to help. They think they are doing something good when it is only creating problems. 
Unquestionably, it is they who are the corrupters, but they perceive [it] not.
Allah (SWT) affirms that they are creating problems and spreading corruption. The sad part is that they don’t even realize it. They continue to justify their wrong actions thinking they are doing something good. But Allah (SWT) says that they are not helping anyone. In fact, they are only harming themselves.
And when it is said to them, “Believe as the people have believed,” they say, “Should we believe as the foolish have believed?” Unquestionably, it is they who are the foolish, but they know [it] not.
When they are told to be good Muslims, follow the footsteps of Muhammad (S) and the Sahabahs and the righteous among them they laugh it off saying should we believe these foolish people? Should we follow these “mullis” or “wahabis” or “religious” people who are too serious and don’t know how to have fun? They are considered foolish because they don’t work for worldly gain and are ready to sacrifice anything for Allah (SWT). Allah (SWT) responds to them saying that indeed the believers are not foolish but these hypocrites are but they don’t even know it. They are ignorant and too occupied to get out of it.
And when they meet those who believe, they say, “We believe”; but when they are alone with their evil ones, they say, “Indeed, we are with you; we were only mockers.”
Such people change faces depending on their circle of friends. When they are with the believers they become “religious” and are “loyal” to them. But when they are with the wrongdoers, those who fall into Shaytaan’s traps, they become like them. They give excuses for being with the believers saying we were only with them to see how crazy they were and to mock them. In simple words, they can be considered fake. 
[But] Allāh mocks them and prolongs them in their transgression [while] they wander blindly.
Because they mock the believers, they receive a taste of their own medicine. Allah (SWT) in response mocks the hypocrites and lets them wander blindly in dunya. Because they chose to mislead themselves, Allah (SWT) allows them to wander away in disbelief.
Those are the ones who have purchased error [in exchange] for guidance, so their transaction has brought no profit, nor were they guided.
These people traded away the guidance they had for misguidance. It’s as if they went to the store and bought 3 packs of misguidance for the price of 3 packs of guidance. They received no benefit from this trade, only loss. They were not guided because they chose misguidance over guidance. They had the chance to follow the Qur’an, but they wanted to have fun in dunya instead.
