Mow the Jasmine weeds. Mowing accomplishes two things. It gives the weeds less time to grow and it clears up the area, making it easier to see what you are doing during the weeding process.
Lightly water the area around the Jasmine weeds. Water will loosen up the soil, making the weeds easier to remove.
Dig around the weed using a hand-held hoe. Hand-held hoes are desirable because, unlike using your hands, you do not have to bend over, thus saving your back. When digging with the hand-held hoe, you want to scrape the soil with the hoe blade nearly parallel to the soil surface. This will prevent you from digging too deep. Digging too deep can bring weed seeds to the surface where they are more likely to germinate.
Pull the weed out of the ground with your hands. Do not pull the weed from the top. Instead, pull from the root ball to ensure that you remove the entire weed.
Fertilize the area. Fertilizer helps plants flourish, thus crowding out weeds. Be sure to fertilize during peak growth times for whatever you are planting in the area-- whether it is grass or vegetables. Fertilizing during dormant times may actually stimulate weed growth.