Jesus taught his disciples to pray with the prayer known as "The Lord's Prayer", even though that is really not the best name for the prayer.
It is not an entirely appropriate name, since the prayer would not be appropriate for Jesus (he had no sins or debts or trespasses which needed forgiveness) but is appropriate for followers of Jesus. So a more fitting name would be something like "The Disciples' Prayer." In the prayer, Jesus teaches us to pray, "And lead us not into temptation" (found in Matthew 6:13 and Luke 11:4). Yet in James 1:13 it clearly says that God does not tempt anyone. So why does Jesus instruct us to pray "and lead us not into temptation" if God doesn't do that anyway?
The word behind "temptation" in the prayer can be translated either temptation or testing. The idea of temptation (in the sense of enticing to sin) does not seem to fit, because of James 1:13. That is, if God does not tempt us to begin with why would we ask him not to tempt us. Yet the idea of testing also has problems of its own. The Bible makes it very clear that we will face trials and testings from the hand of God, and when we do, we are to receive them with joy (James 1:2, 1 Corinthians 10:13, Psalm 71:20). So to pray for grace and strength during a testing would seem appropriate; but to pray for testings not to come our way would not seem exactly right either.
So here are two possible solutions. The first possible solution would be to understand the word in the sense of testing, and the prayer would then ask God to not bring difficulties our way. This would be consistent with the fact that Jesus told his disciples to "rejoice and be glad" when they face persecutions (Matthew 5:11-12), but yet told his disciples to flee persecution (Matthew 10:23) and to pray that their flight might not be too difficult (Matthew 24:20). God tells us to receive trials and testings with joy and faith and trust in his sovereign plan; yet he never tells us to seek out trials or to not seek relief from hardships. So we can ask the God not bring testings our way, but when they do come, "consider it pure joy."
The second possible solution would be to understand the word as temptation, but to put an important comma between the phrases "and lead us" and "not into temptation." The Greek in which the New Testament was written does not have any punctuation marks (or spaces between words for that matter), so any punctuation marks in your Bible was decided upon by the translators. The prayer then asks God to lead us, but rather than positively saying the direction that God leads us (as in "paths of righteousness" in Psalm 23:3), it gives us the negative direction of where God will not lead us. Imagine that we are in Missoula and you want me to drive you to Kalispell. You could ask, "Drive me to Kalispell," or you could ask, "Drive me, not to Hamilton." The first request is more specific, but both would be true. In this sense, we pray, asking God to "lead us, not into temptation," but "into paths of righteousness for his name's sake."