Illegal move + Clock Button Press

If my opponent doesn't see a check or any other illegal move and make a move and then press the button on the clock. What should we do then?

We are amateur players just starting to play timed games. And I think this type of problem will arise many times in our games. Any solution for this?

Just point out your opponent made an illegal move and reset the position before the illegal move.

but if he quickly makes a move and press clock. Then my clock will start ticking. And then my 5-10 seconds will be wasted telling him about his illegal move.

if you're just playing casual games do what JMB2010 said.

If your goal is to prepare yourself for a tournament, you might give the offending player a time penalty appropriate to the time control, as this would simulate tournament conditions and would encourage you to learn not to make illegal moves.

Use time delay.

hmm ok thanks everybody

googling time delay.

if he makes an illegal move, just quickly hit your clock and tell him how his move was illigal on his time.

In blitz you take the your opponent's king and you win

Taking the King IS illegal, also in Blitz. So if you don't claim the illegal move by your opponent, and take his King instead, your opponent can claim and wins the game.

(That's how the current rules are in the Netherlands and I suspect it's the same worldwide)

When opponent makes an illegal move, you should be rewarded with 2 minutes of extra time. 

Third illegal move loses the game. 

Unfortunately, at least around here, it is not uncommon that this rule is abused though (in extreme time trouble, when an accurate move is needed to avoid mate or loss, make an illegal move and think while opponent calls the arbiter).

In the USA taking the king is equivilent to making an illegal move claim, you win if you take the king.

Stop the clock, then point to the King. or Take the King and stop the clock. If the flag falls, and you both didn't see it, it's a draw.

What do you mean by "if the flag falls"

On analog chess clocks, the start of the new minute is determined by a flag placed near the 12 position. When the second hand touches the flag, it raises it. When the hand lands on the 12, it falls - the game ends or a new minute starts. 

Your flag falls before you claim your opponent King. But both of you didn't know that your flag has fallen. You don't have a flag, and your opponent doesn't have a King. It's a draw.