When I think to myself, I have a running dialogue in my head. If someone has never heard a voice before, how do they think?
How a deaf person thinks depends on what kind of exposure they've had to language and life in general. A deaf person who has no hearing at all or who has never heard speech in any way doesn't know what voices or speech sounds like. Someone who has some hearing and can hear parts of speech does know what voices and speech sound like, but their idea of speech and voice is different from a typical hearing person's.
For deaf people who have never heard speech, they think in the same language that they use. A deaf person who uses sign language will think in sign language, and will "see" the signs in their mind's eye the same way hearing people "hear" a voice in their mind's ear. Similarly, a deaf-blind person who uses tactile sign language "feels" the signs in their hands in the same way a deaf person "sees" the signs in their mind. A deaf person whose main exposure to language is in its written form might visualize their thoughts like print on paper or handwriting on paper. Many deaf people also say they think in images or just concepts in general, independent of language. Of course the details of how a particular individual thinks varies, but deaf people can and do think independent of sound (and language when they've had little or no exposure to language).
When I think of a word, I imagine it written on paper in my head. How does a blind person visualize the spelling of a word?
Depending on the writing format they use the most, a blind person might also visualize a word or its spelling in print. If the blind person uses braille too, they can "visualize" the braille in their heads, in the same way as print. Some blind people "feel" the braille under their fingers in the same way a sighted person "sees" a word in their mind.
There's a lot of variety in how people think so the ways mentioned above aren't necessarily the only ways people think.
How do deaf, blind, and deaf-blind people dream?
People's dreams generally reflect their reality. Whatever extent of hearing loss or vision loss a person has in real life will generally experience the same in dreams. Whether or not a person was born blind, deaf or went blind or deaf a long time ago also makes a difference. Someone who is born totally blind cannot visualize images. Someone born totally deaf cannot conceive of sound.
Both totally blind and deaf people can conceive of sound and images in different ways though. Some deaf people have visual associations with sound (such as moving lips) and also an association with vibrations. Blind people can "visualize" through their sense of touch, where their brain forms an "image" from tactile information. A blind, deaf, or deaf-blind person may also experience smells and tastes in their dreams more often.
People with progressive vision or hearing loss may either still be able to hear or see in their dreams, or their dreams may reflect their progressive loss with a delay in time.
Sometimes deaf or blind people mention having a sense of "knowing" where things are in their dreams even if they may not know where things are in real life. Some deaf people also mention a sense of telepathic communication or communication free of language in their dreams. Some deaf people also mention that their dreams come with automatic "closed captions" for all the dialogue in their dreams. Deaf people who use sign language often experience the people in their dreams signing, regardless of if the person knows sign language in real life or not.
Because of the variety in how people think there might be other ways that deaf, blind, and deaf-blind people dream that haven't been mentioned here.