I have just started to study the concept of a renormalizable theory in Weinberg's feild theory book. I am not sure if my understanding of the process is correct and would like some additional explanation or corrections; As far as I understand in any theory there will be unrenormalizable interactions, however these infinities will be removed if we add all possible interactions allowed by gauge and lorentz symmetry to the lagrangian. I firstly don't understand how this process exactly works. Secondly it appears to me that it is then claimed that even in an unrenormalizable theory such a lagrangian will lead to finite interaction terms and this part i really don't get, but i am not sure if i have just misunderstood this. Any help would be greatly appreciated.