They have to organize the bachelor party and they have to deliver the best man speech at the wedding. Some folks may not like public speaking but if one is prepared then they can really have a great speech.
If you fail to plan then you plan to fail. I know that you have heard that before but it is so true when it comes to the best man speech. With all that is going on, the best man should get the speech ready 2 to 3 months in advance. There will be so many distractions happening so its best done right away.
Only make jokes about your groom and leave the new wife alone with your jokes. She will get her turn with her maid of honor. Do not revel too much about the groom but some stories need to be shared while others should be left alone.
Practice.. Some folks are awesome speakers while others not so much. But with dedicated practice then the speaker can at least look the part. Practice the speech in front of the mirror. Also, maybe have someone record you on your phone. You don’t want to talk to fast and you want to make sure you sound good. Speak slowly. One trick of the trade I used is really move your lips when you speak each word. They come out clearer than ever. Maybe practice in front of some trusted friends who can give you feedback.
Don’t try to wing it and not have your speech not written down. It does not need to be written down word by word but at least be in bullet points. I would also have the notes on your phone in case your notecard gets lost in the shuffle of the wedding.