The immediate symptoms suggest a classic conjunctivitis (infection and inflammation of the pink membranes around the eye) that we know commonly as "pink eye". If the only eye affected is the left and there are no other symptoms such as sneezing, coughing, poor appetite, or scratching around the face, the problem should be easier to fix. However, this will still likely require a vet visit since even topical eye antibiotics often require a prescription and prescriptions require a doctor's involvement.
You can help your kitten in the meantime by simply cleaning the caked, crusty or "goopy" discharge around the eye with a warm water soaked wash cloth being careful not to rub too hard or accidentally rub against the eye itself. Do not attempt to use human eye products like Visine or Clear Eye since they can actually harm the eye in cats and do nothing for infections, which are usually responsible for the greenish "gunk" that accumulates.
Your vet will likely test the eye surface (or cornea) for the presence of any scratches or scrapes that will show up using a special ultraviolet light. This should be done if recommended by your vet since the medication chosen may differ if there is corneal damage. If not, a topical antibiotic +/- an anti-inflammatory will likely be sent home and in 3-5 days, the symptoms should be much improved.
If there are other concurrent symptoms such as respiratory signs then an oral antibiotic may also be recommended or therapy aimed towards possible viral involvement as viral infections in kittens are common and often involve the eyes as well as the nose and throat.
Hope this helps,
SoCalPetDoc
Cat Veterinarian
7yrs in family practice, internal medicine, surgery, and geriatrics for both dogs and cats