How does shrinking a SQL Server log file affect performance?
I really recommend reading Importance of proper transaction log size management by Paul S. Randal.

The quintessence is that there are only two really good ways to do transaction log handling:


Either go with regular LOG file backups and the LOG-file will reuse it's space after each LOG backup and won't grow indefinitely, or
Use the SIMPLE recovery model and you don't have to care about your LOG-file size, as you do regular full backups.


What concerns LOG-file truncation and performance is that you will always get a performance hit when the LOG file is to be increased (a quote from the above-linked blog post):


  If you shrink the log, then it's going to grow again - possibly causing VLF fragmentation, and definitely causing your workload to pause while the log grows, as the log can't use instant initialization [...]


Update: Don't mistake LOG file truncation for DATA file shrinking. DATA file shrinking is really bad. See Why you should not shrink your data files for details.