This passage has always been a hard one for my prone-to-worry spirit. Seeking first the kingdom of God and his righteousness seems simple in theory, but it's a little more difficult in practice, isn't it?
Seek first the kingdom of God
It's easy to get caught up worrying over bills, deadlines, appearances, and desires. But if I remind myself that my citizenship isn't on earth but in heaven (Phil. 3:20) and I am more careful to please God while continuing to work out my salvation (Phil. 2:12), I will be less worried about pleasing myself and other people.
And his righteousness
Righteous is probably not the first word I would use to describe myself, especially when I think about all of my daily struggles. But righteousness is granted to us by Christ and should be pursued by us as well. By pursuing righteousness, the comforts of this life become less desirable and all my unnecessary concerns begin to fade.
And all these things will be added to you
We've grown up being taught to strive after the American Dream - that all of our needs and wants will be granted to us if we work hard. And although there is an element of truth in that, our works should not be where we place our trust. The American Dream runs contrary to what Jesus is teaching in this verse: if we seek the kingdom of God and his righteousness our needs will be met. They may not be met in the way we hope or expect, but he promises that he will meet them.
A Word of Encouragement
We can seek the kingdom of God. We can pursue righteousness. 2 Corinthians 5:21 says, "For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God." If we seek the kingdom of God and his righteousness, our worries will fade and our needs will be met.