Some fish indeed have live young but goldfish are members of the carp family and lay eggs. To encourage them to breed you need one female and two or three males. The female will only release her eggs among plants when a male pushes against her side and as she releases the eggs the male will release milt which mixes with the eggs and so fertilises them.
When the intense 'chasing' has lessened you can grab some of the plants where you've seen them breeding and put them in a bucket without lifting them out of the water, thus keeping the eggs in the same water.
Put the bucket under cover but not in the sun. If successful you will see very small needle-like babies hanging on the side of the bucket after a few days, which will start swimming two or three days later depending on the temperature.
Get some proper food from the petshop. Live food such as just hatched brine shrimps is best but hard to get. After 2 weeks take up to 100 or so of the biggest young and give the rest to friends. As the fish grow you need to keep splitting them up as when they are 1" you should not have more than 10 in a 2 gallon bucket or their growth will be stunned.
Have a go, it is lots of fun.