Depends, for an example: an alliance came to stage in our home system and as a small group 1/10th their size we where picking them off and winning the isk war xD so we got invited in. I’m sure it’s different for every group so just be awesome and someone will send you invites.
Avg case would probably be that your corp kill board shows that your corp is very active and decent at pvp, if you put your self in the shoes of an alliance they would be looking for people to increase their strength without increasing their losses much so avoid silly losses , use out of corp hauler alts and such to remove those losses from your kill-boards. If you train new guys make a feeder corp so they don’t paint your killboard’s red and bring them in when they are trained up.
There are some alliance’s that look for your risk adverseness so if your constantly bringing ecm to fight’s or cyno dropping they will not consider you, but then others will because they like that kinda stuff so do what ever you like man and chance’s are you will find an alliance that has the same play style as you corp’s.
Out of interest do you have an alliance you are eye balling and would like to join? Also another good way is to post on forums say how active your corp is and what is your preferred play style and you will get tons of invite’s from a whole bunch of alliances.