In as much as I have not faced overt persecution for my faith, I had always assumed that this verse did not apply directly to me--except in the sense that I had to be willing to suffer with Him. However, I do not think that any more. I think suffering is a normal part of the Christian life no matter where one lives or under what circumstances one lives in this deeply broken world.
Suffering with Christ is keeping my mouth shut when I desperately want to say something, but I have nothing specifically edifying to say. Suffering with Christ is speaking when I should speak, but when remaining silent is safer. Suffering with Christ is saying no to my wandering desires and to my never-satisfied body even when my body and mind seem to be screaming for satisfaction. Suffering with Christ is being kind when I am tired and annoyed. Suffering with Christ is hiding the sins of others and confessing my own. Suffering with Christ is keeping silent and trusting God when I am misunderstood and wrongly accused. Suffering with Christ is saying prayers and fasting when no one but God knows. Suffering with Christ is loving those difficult to love.
Of course, suffering with Christ is also enduring overt persecution for Christ's sake--or because you are poor or handicapped or not considered beautiful, or because you are of a different race or cast or political party than those around you. All of this is suffering with Christ, who became poor and weak and despised and an outsider for our sake. When we suffer for any reason and we offer that suffering to God, we are suffering with Christ.
As Christians, all that we have and are belongs to Christ. This includes our weaknesses, most especially our weaknesses. It is easy to offer to God what we perceive to be our strengths. Heck, even Pagans do that. But to offer to God our weaknesses, to offer to God our suffering--especially if it is suffering we are ashamed of, suffering that we know comes from our sinful weaknesses--this is a major step in our growth in Christ. This is the true experience of sonship, of becoming childlike; for what three-year old hides from Papa his suffering, no matter what its cause?