How much will a poor first semester affect my grad school chances?
If a student did poorly in their first semester of college, but did well afterwards, admissions committees will conclude that the student learned from what ever problems they had the first semester, and will be unlikely to perform poorly again.  However, if they can choose a student with a perfect record, they will.  On the whole, first semester grades are of little importance except at the most selective institutions.

If you explain in your application what went wrong, why it will never happen again, and how it made you a better applicant, it may strengthen your application.

(us perspective)