When do we use a two-tail hypothesis testing instead of a one tail? I always use a two-tail hypothesis testing unless I am told to use a one tail. Is that a good way of going about solving problems or is there a flaw to that way of doing things?
Also, if they say use a significance level of a = 0.05, does that mean I can choose 0.025 and do a two-tail or a one-tail with 0.05 or does that mean i can only use a one-tail test?

Whether you do a one or two-tailed test is dependent upon the experiment.  A two-tailed test implies that your error is symmetric around your expected value, which is often the case.  A one-tailed test implies that your error is in one direction.  This is not often the case, but it could be.  So ... to the experiment!
