Your sentence can be translated in two ways: by using a relative pronoun and by using a relative participle. Relative pronouns work in the same way in Hindi and English.
There's no one here that can read. - यहाँ कोई नहीं है जो पढ़ सकता है।
The indicative mood (सकता है) can also be replaced by the subjunctive mood (सके): यहाँ कोई नहीं है जो पढ़ सके।
There is little difference between the two forms and you can say either. I feel the latter gives a more "diffused", as in, generalized, nonspecific, account of the inability of the people in question to read.
Hindi just uses a distinct set of words for relative pronouns (all starting with ज), unlike English, which uses interrogative pronouns and "that".
A relative participle is basically a verb phrase modified to act as an adjectival phrase (or noun phrase). These are quite common in Hindi and often not directly translatable into English. I'm rewriting the Hindi sentence with the relative pronoun first and then giving the other construction.
यहाँ कोई नहीं है जो पढ़ सकता है। - Relative clause in bold, containing and starting with the relative pronoun जो.
यहाँ पढ़ सकने वाला कोई नहीं है। - Relative participle in bold. Here, the verb पढ़ सकना (to be able to read) has been modified into an adjective form by using वाला.
Translating the above sentence word for word won't give a meaningful sentence, so here are some simpler examples to help understand how the relative participle works.
चिल्लाने वाला लड़का। - The boy who screams. (चिल्लाना - To scream)
उड़ने वाली बिल्ली। - The cat that flies.
यहाँ आने वाले लोग। - The people who come here.
अपना काम नहीं करने वाले। - Those who don't do their work.
यह घर चल नहीं सकने वाले लोगों के लिए है। - This house is for the people who cannot walk.
यह घर चल नहीं सकने वालों के लिए है। - This house is for those who cannot walk.