You can only invite new members to a consulting room when you have got propper rights. Whether you have those rights depends on the settings of the room. If the owner of the consulting room (the one who started the conversation) has changed the settings so that only he / she can invite new people you will have to ask the owner to do it for you.
If you do have the required rights, in the web interface you will see a blue circle with a white plus in it above the list of room chat participants on the right. When you click on the plus you can pick contacts and / or colleagues to invite.
On your mobile device you can invite new people by going to the menu in the top right corner of your group chat and
choosing ‘options. You can then click ‘Add participants’ in the ‘Participants’ tab.