You can run regression models separately, if you follow the Baron-Kenny approach. As far as I know, there are two general approaches to test for mediation: (1) path models (and, SEM, of course) and (2) the Baron-and-Kenny approach (see item (a)). I use Mplus to run my mediation models which is very handy (+ bootstrapped standard errors).
Unfortunately, you did not tell us what software package you are using to do your analysis. You have a couple of options:
(a) You might be interested in D Kenny's website on mediation . He gives a very clear description how to proceed in order to test for a mediation effect (see "Baron and Kenny Steps").
(b) If you happen to use Stata or R for your analysis, you could check out the ATA website on Stata Frequently Asked Questions (search for 'mediation') or the R package mediation. If you use SPSS, you will like this website. Kenny's website also offers a couple of tips for different software packages, e.g. how to get bootstrapped standard errors in SPSS or SAS.