There are 3 ways to gain companions in this game.
If you play with a clan that has a Social Discipline and you invest in that discipline, you will be able to enchant, dominate or bend the will of several humans into being your servant. The level required depends on the quaity of the human. Bums and Prostitutes only require level 1. Normal humans require level 2. Ghouls and other enhanced humans require level 3.
Social disciplines include Domination, Dementation and Presence.
Domination: Available to Tremere and Ventrue
Dementation: Available to Malkavian
Presence: Available to Brujah, Toreador and Ventrue
In CompMod, Presence is considered weaker than Domination or Dementation and therefore requires an additional level to accomplish the same feat. For example, to make a Bum your servant requires a Presence of Level 2, but only requires Domination or Dementation Level 1.
Social Disciplines will not work on undead such as Vampires. For more details see the Spoilers section.
Some NPCs will willingly join forces with you. Later in the game, you will be given the opportunity to embrace one human. Embrace options are limited to those humans who willingly join forces with you. For more details see the Spoilers section.
Towards the end of the Alistair Grout quest given to you by LaCroix, you will discover the Animus Constupro. The Animus Constupro (AC for short) is a parasitic creature that has the power to enslave anyone, even the most powerful Vampires. However, the creature has been trained so that it only releases its enslaving venom when someone feeds from it directly. Therefore, you must actually convince others through dialog to drink the creatures blood in order to enslave them.
If you are playing with a clan that has Social Disciplines, you can try to use Mind-Control on Vampires to make them drink the blood, but most vampires will shrug off the attempt. It will only work if you catch them off guard by doing it to someone who trusts you.
There are other ways to get vampires to drink the blood. Trickery, persuasion and timing are tools of the trade. For example, while a Vampire may not trust you, often times Vampires have Ghouls or allies that they DO trust. If you learn the identity of these people and then possess their allies, you can often trick a Vampire into drinking blood under false pretenses.
The Animus Constupro offers party building opportunities to all clans. Once you use the Animus Constupro to gain some Vampire companions, you can then possess those companions and use their powers to gain human companions that you previously did not have access to. It also allows easier enslavement of humans once it is in your possession, lowering the required discipline level by 1 point through new dialog options. (Very handy for clans that rely on Presence).