Here's the list of Dallas Stars draft picks in this year' NHL Entry Draft.
1st round: 14th overall
2nd round: 44th overall
4th round: 105 overall
5th round: 135th overall
6th round: 165th overall
7th round: 195th overall
The Stars technically also own a third-round pick (75th overall) in the draft, but right now that will be going to New Jersey as part of the Jamie Langenbrunner trade. It was a conditional third-round pick, and here are the conditions as they stand right now.
If the Stars do not sign Langenbrunner before the draft then New Jersey gets that third-round pick in this week's draft. If the Stars were to sign before the draft (and that is not going to happen) then New Jersey would get the Stars' second-round pick (44th overall).
If the Stars sign Langenbrunner after the draft then the Stars also would swap their second-round pick for New Jersey's third-round pick in next year's draft.