If you notice your conservation is getting awkward, try some of these tips.
Change the topic: if you become uncomfortable with a topic, change it before the conversation become awkward.
Do something to lighten the mood: You can do this by telling a funny joke or story, poking fun at yourself. This will help easy the current mood.
Exit the conversation: if you are uncomfortable and there's nothing else to talk about, it is best to leave the conversation. While trying to leave the conversation, do it politely and if the other party doesn't understand that you need to leave the conversation, kindly excuse yourself. Give an excuse that you need to use the washroom or you need to get another drink.
I think the answer to this question might depend on what’s awkward about the conversation. For example, if the person is making you feel uncomfortable, you might seriously consider saying something like, “I’m sorry but this conversation is making me feel very uncomfortable and I am going to stop talking with you now”.
Then, walk away and find someone else to talk to. If you think the conversation is awkward because the person to whom you’re talking is just not a good conversationalist, you can make an excuse to stop talking with them. The best excuse is that you need to make a phone call because most people won’t follow you choosing to respect your privacy. If you make a different excuse such as I need a refill or I’m going to the buffet table, the awkward conversationalist may follow you.