There's a lot of good advice out there for PhD students, but this list is not about advice; instead it is about reassurance. The first couple years of your PhD can be the most difficult for some people. This may be a time when you have not published any papers yet and are asking yourself "am I cut out for this?" Here are three pieces of reassurance based on my own experience so far in TCS:
1. When you start publishing is irrelevant. Some PhD students hit the ground running and publish early. Others write their first paper in, say, their third year or later. Although it may be difficult to spend several years at the beginning of your PhD without any publications, it is not predictive of your future career.
2. Your speed of thinking is irrelevant. You may feel pressure to think quickly on your feet to "sound smart" in meetings. However, this ability is orthogonal to succeeding at research. Successful researchers come in all types, fast and slow. It is fine, and often beneficial for everyone, to ask other people to slow down.
3. It's ok if you can't do an "exercise". As a PhD student you encounter "exercises", either in the form of a homework problem, or when a research collaborator says "this is a good exercise". After thinking about the exercise for a while and not solving it, you may think to yourself "If I can't even do this easy exercise then how am I ever going to contribute to research?" But the fact is, sometimes you can't do an exercise even in your own field, but you can solve a research problem, and that's just the way things work.