Basically, all you have to do in order to get the YouTube video to start at a certain time. is to first find out what point you would like the video to start at. Once you know when you want to video to start, you just add the time to the end of the YouTube video url in a certain way.
For instance, if there is a video at a certain url:
...and you would like to link to it such that when the link is clicked, the video will start playing at the 1:51 mark, then all you would need to do is to add the starting time at the end of the link like this:
And that is it. That is all you need to do to link to a YouTube video, having it start playing at a certain specific time.