"Was I fickle when I intended to do this? Or do I make my plans in a worldly manner so that in the same breath I say both 'Yes, yes' and 'No, no'?" NIV translation
Paul uses this question to get them to see that it is not about his plans but about listening to the Holy Spirit. He intended to do this but his actions were always subject to the leading of the Spirit. This is what James was talking about when he said that we should always make it known that our actions are subject to the will of God (see James 4:15).
"But as surely as God is faithful, our message to you is not 'Yes' and 'No.' For the Son of God, Jesus Christ, who was preached among you by us - by me and Silas and Timothy - was not 'Yes' and 'No,' but in him it has always been 'Yes.'" NIV translation
Paul reminds them that it is all about Jesus and sharing the gospel.
They had heard the gospel because of the efforts of Paul's ministry team and that was the main thing.
"For no matter how many promises God has made, they are 'Yes' in Christ. And so through him the 'Amen' is spoken by us to the glory of God." NIV translation
The word "Amen" means let it be so and Paul is describing the fact that our will must be conformed to the will of God. We can make all kinds of plans but the only plan that really matters is the plan of God for our lives. We can only know and follow that plan through the power of the Holy Spirit that is active in our lives.
"Now it is God who makes both us and you stand firm in Jesus Christ. He anointed us, set his seal of ownership on us, and put his Spirit in our hearts as a deposit, guaranteeing what is to come." NIV translation
Paul goes on to explain that we all have that same Spirit living in us and we should be able to understand walking in the Spirit. He reminds them and us that the Spirit living in us is our assurance of eternal life with God. We are secure in our salvation because we know that the Spirit is in us. Therefore, there should be no way that anyone or anything can get you to question whether you are saved or not.
"I call God as my witness - and I stake my life on it - that it was in order to spare you that I did not return to Corinth. Not that we lord it over your faith, but we work with you for your joy, because it is by faith you stand firm." NIV translation
Paul had already made one difficult trip to Corinth and he says, here, that his plans changed so he did not have to do so again. In short, he gave God a chance to work in the hearts of the believers.