The key of D has 2 sharps, f# and c#.
Note that when going 'up' in the circle of fifths, the sharps from the previous key (in this case f# from G) remain and one sharp (C#) is added.
Here are the chords of D.
Or, in another voicing:
As an exercise, play 'My Bonny' in D (without the transition chord to A7 - that would be E7 and we haven't covered this yet)
Another well known song is 'When the saints go marchin in'.
We will play it in C, with a transition chord that 'wants to go to' F - a C7.
(C7 is the fifth degree of F, we will get to that).
As you notice this transition chord is the root chord (C chord), with a 7th added (C7).
Why C7 wants to go to F? Again, because C7 is the 5th degree of F.
The general rule is, if you are looking for a chord that wants to go to chord X, find the 5th degree of X.
We have learned 2 transition chords now in the key of C:
C7 to F (transition chord to IV)
D7 to G7 (transition chord to V)
We can play them in a sequence like this:
Exercise: play 'When the saints' in G, with the transition chord to IV (which is C).
What transition chord is that? Well we learned that it is the root chord with a 7th, so that would be G7.