"No temptation that comes your way is beyond the course of what others have had to face. All you need to remember is that God will never let you down; He'll never let you be pushed past your limit; He'll always be there to help you come through it" (1Co.10:13 MSG). Most translations say that God will provide a way of 'escape' along with the temptation. Some people think this means God would take away the temptation itself. God does that at times. But most often He allows us to face temptation so that we can come through it as a better person, a little more mature and a little more like Jesus.
How does He help us to go through the time of testing? This is where His love and wisdom come in, to give us the right type of help that we need, not only to deal with our situation but also to give us the training we need at that particular point in our life. This could be to comfort or encourage us, or to challenge us to put off the things in our life that are holding us back from making progress and becoming what He wants us to be. He may do this by reminding us of some word He has spoken to us before, by blocking some path we expected to go in, bringing someone into our path to tell us something or to make us think in new directions, etc.
One mistake we make is to expect God to do for us what we figure out is the best thing. Sometimes we think He will do what He did for us earlier or what we heard He had done for others. People mistakenly think that this is what He.13:8 means! But God custom designs His help for each one of us! His goal is not for us to escape from the situation but to endure or bear the temptation. This means that in the end we come out on top of the situation rather than crushed under it. We are not to get damaged through it but come through it better off than when we entered it.
Our understanding of what God wants to do in us makes the difference in how we face situations. If we are waiting to escape from them, we may beat our head against the wall and get hurt finally. But if we are looking out for learning what He wants to specifically in each situation, we can look in the right direction. Even if we can't figure out what exactly He is doing, we can go through by trusting Him and holding on to Him. Perhaps later on we may be able to look back and understand what He accomplished in us.
Let us remember that the essence of every temptation is for us to make a choice for God against our own desires or preferences. Therefore it would mean that the right way to go through the temptation would many times involve giving up something from our side in order to receive what God is offering for us. Even though God is mindful of our earthly needs and He provides them for us (Mt.6:31,32), we should not miss out the eternal lessons and transformation that He wants to give us through our daily situations (2Co.4:17). For that, our heart must be looking at Him to see what eternal work He wants to do in us (Co.3:1,2).