The vast majority of tortoises kept in captivity have bright black eyes and generally look a little shiny. There are however a few exceptions to this. The main exception being box tortoises, their eyes tend to be orange, brown or yellow which blend in well with the camouflage markings on their heads. All tortoises have very good colour vision despite there being no blood vessels on their retina. Unlike mammals there are no tears ducts to the nose, so any tears that may appear roll down their face.
Tortoises also have a third eyelid which is usually very difficult to see and is only slightly visible at the front corner of their eye. It usually becomes more visible or obvious in tortoises that are diseased or dehydrated due to the eye slighlty sinking into the head. This is usually also be accompanied by the incomplete opening of the eyelid.
If your tortoise is completely awake and warm and one eye remains completely closed, it needs to be opened to establish whether there is a problem with the eye. It is sometimes possible to do this by using some warm boiled water to soften the eyelid. Again this can also be used to help ease eyelids open if they are sticky after hibernation. The lower eyelid is more mobile than the upper eyelid which is quite firm and almost fixed in place.
A fairly common problem can be that there is some plant material in the eye or on the surface of the eye. Once again some warm boiled water can help to flush this out of the eye. It may need gently teasing out, which would need the surface of the eye to be flushed with antiseptic eye drops like Brolene, which is generally available from checmist. For me, if it where to get to this stage I would seek advice from a vet before going any further and would be keen to get them to deal with it as to minimise any possible damage to the eye.
Another problem that can occur is swollen eyelids. If this appears on one side only it may be due to an injury such as a scratch from another tortoise or a burn from a heat lamp if they have been allowed to get to close, it could also be caused by an infection. However if both sides have are affected, this could be due to a Vitamin A deficiency. Some of these conditions could be caused by debris in the eye, which could be flushed out with some warm boiled water, there could also be a white plaque like substance on the cornea of the eye. In all of these case it would be advisable to seek treatment from a vet.
Cataracts or even cloudiness of the eye may have been caused by freezing whilst the tortoise was in hibernation. Many problems can be caused by this such as strange behaviour and difficulty eating. Some mild or minor cases can return to normal over time, but will probably require treatment as well as hand feeding for a year or more. As with anything prevention is better than cure and it is easier to prevent a tortoise from being subjected to this fate by making sure that your tortoise is hibernated in a frost free place inside a well insulated box.