Dysgraphia is a blanket term for difficulty in written communication and producing the written word, generally with an onset in childhood. The term dysgraphia is generally understood to encompass a variety of conditions with seperate causes and symptoms, but all of them, obviously, share this interference with writing.
Probably the most common situation that dysgraphia occurs in is comorbidity with other learning disabilities, particularly dyslexia, and sometimes ADD or Asperger's Syndrome. In this case, the problem is probably a result of general problems in the parts of the brain responsible for processing the written word in general, and the symptoms of this sort of dysgraphia tend to reflect that: transpositions of letters and words, the mixing of upper-case and lower-case, as well as cursive and print letters, and confused production of similarly-shaped letters. There's no real cure for this form of dysgraphia other than lots of practice, slow and careful writing, and even more careful proofreading.
The dysgraphia through poor fine motor coordination that sleeping wolf describes above is another common form. The technical term for the poor coordination that he talks about is developmental dyspraxia, and dysgraphia caused by it will indeed be manifested largely through very sloppy handwriting, and problems in properly holding and controlling a pencil. The treatment for this form of dysgraphia is both obvious and largely successful: simply do as mucb writing as possible on computers and word processors.
Developmental therapists sometimes include another form of dysgraphia, which they refer to as non-specific dysgraphia. In this case, the difficulty in writing is not from some specific neurological condition, but more generalized and often environmental causes like poor or no instruction, and general poor performance in school. In this case, treatment usually takes the form of sessions with a handwriting tutor, or some related therapist, and the prognosis varies widely with individual circumstances.