It depends on what kind of morning glory you have. If it produces seeds, pull it up and then pull up any seedlings you see. This will take several years of constant observation of the area.
If it is the weed called "bindweed", use Round Up or something similar on every bit of it you can see. Shield other plants from the spray with cardboard or you will kill them also.
If it is the seedless, blue morning glory, also called "Ipomea", well, good luck. This one propagates itself by sending down roots from every runner that touches the ground. You can try pulling it up and/or using Round Up. If it has gotten into a hedge or bush where you can't reach it without destroying the hedge or bush, you are just stuck with it.
Add your voice to the conversation. Click here to answer this question.