Any DIY retail outlet will stock gutter sealant - i.e. black mastic in a tube - for sealing gutter joints. You can use it on any type of gutter.
The least you will have to do is remove all dirt and water from the joint and apply to the leaking area but to do a good job you would need to dismantle the joint, clean & dry all the mating surfaces, apply the sealant and re-make the joint. Easy enough to do.
However, if the gutters are old cast iron or steel, the joints will involve bolts which more than likely will be well corroded and will have to be cut off using a hacksaw or a cold chisel and hammer. Again new gutter bolts can be got in any hardware shop or DIY outlet.
JD
March 2008