By talking about something really interesting that applies to your crowd. Know your audience is rule #1. NOTE Some people will tune out easily when hearing a regular scholarly vort on the Parshah or Halachah. You should not use such ideas on that crowd. You should instead focus on heartwarming stories and aggadata.
By opening up with a statement that is outrageous or catchy in the first 3 seconds. There are many styles to achieve this.
Actually it gives respect for the thing about to be said. Even people attending secular awards dinners, stop eating, to hear the next speaker because its the important focus of the evening. But, you can make sure to speak on a topic that touches on "real life".
Don't sound like you are trying too hard. It becomes condescending. Secondly, maybe the crowd you have that night is not ready for a vort but is ready for a story or topic that happened to you in the week which teaches how a Jew should act/make a Kiddush Hashem etc. (maybe even with humor and a twist?)
In general, you are not the thought police. If you are giving a vort to make sure people "speak Torah" by the meal, it may be resented and the opposite effect will happen; namely, people won't want to learn Torah. Be humble and only speak about something the crowd wants to speak about and then build in a Torah vort they can handle and appreciate.
The Lubavitcher Rebbe said constantly: "Words that leave from the heart, enter the heart." If you are saying the vort because you actually care about the peoplel listening, then they will know. They will listen in return. If you are just doing it to be "yotzei the chiyuv" of "diverei Torah" at the meal, then people will know it and they will most likely tune out.
So, you may wish to start by simply asking your guests/friends about their week/life and comment about yours too, show sympathy, and be interesting in general. Then go for the vort when you have an opening. OR... Simply ask one of them to share a vort or Torah themed story! Turn the tables. People get excited when they are the speaker. :)
Also, avoid monotone voice. Raise and lower your pitch slightly when speaking as well as slow down and speed up every so often. It stops people from dozing off. Oh yes, and keep it short LOL (2-3 minutes maximum). Also, use humor! Torah should be joyful. Its also contagious to laugh. :)
Do not: "Gut Shabbos everyone... this week's Parshah" (You already lost them!)
Do not: "Rabbi Choshuv Huffenpuff wrote a peirush on blah blah...he asks a great question..." (again, you let them fall asleep here!)
Do Say: "OK folks, I have absolute proof that Ivanka is Jewish!" (insert joke) OK OK, So why does everyone in the media care if she is or isn't? We.. go on about the uniqueness of the Jewish people etc.
Do Say: "Mrs. Mosko-noodlewitz...(The hostess) I can't believe you did this to me!! GASP!!....(wait 2 seconds for crowd's nervous tension and shock) The chocolate pie is killing my diet Its not possible to resist this sin!" :) "By the way, thank you for making the whole meal and all the Sabbath prep that you did for everyone, just for me." Why not for the other guests? Well the Gemara says a good guest says...they did everything just for me..how does that work? ...Vort
Dovid Kaplan has a nice (6 books?) series called Impact and Major Impact. Hundreds of great Torah short stories. You should read it. https://mostlymusic.com/collections/vendors?q=Dovid%20Kaplan
That should work. :)