[PhalPal]

Your biggest problem is not the roots, it's the mushy leaves. Make sure to isolate the plant from your other orchid(s). It is probably a bacterial rot and you will get that from lack of air circulation and allowing drops of water to collect in the crown of the orchid. It could be it was infected from the grower before you got it, since the rot seems to have started at the tips and not the crown. (transmitted by touching) Cut off all affected areas with a single edged razor so you can toss it and not infect something else at a later date. If the leaf is turning yellow just pull it off, there is no saving it.

Soak your root ball in some water for 15-20 minutes and remove as much moss from around the roots that you can. All you need is one good root for your plant to have a chance, so cut off any black mushy ones. If you don't have a new, clean pot you can sterilize your existing pot by soaking it in a 10% bleach solution for 10 minutes and scrubbing off all plant matter. Make sure it has drainage holes on the bottom of the pot. Use new potting soil (whatever you have available) and re-pot your orchid.

There are lots of products you can use for bacteria and fungal infections. I don't know what your budget is or what supplier you have available to you. We can all let your know about our favorites if you are interested. In any case, the above is a good start!