Tours can easily be arranged in Jungut Batu town, but it is just as easy to ride up to the mangrove forests yourself (just take the road and follow it till you can't go any further) and arrange a deal with one of the boatmen right there.
Once arranged they'll paddle you through either in a jukung or sampan. This is a good trip to do with kids.
Early morning and late afternoon are the best time to do a trip as you'll see far more birdlife but you need to keep the tide in mind. Allow for an hour on the boat.