As you already know, CY62256N does not have a clock input and cannot be used as a synchronous device. To perform read and write operations to this asynchronous SRAM, you have to control the following signals CE#, WE#, OE#, Address and Data signals as described in our datasheet, https://www.cypress.com/file/43841/download. If you want to access our SRAM w.r.t clock, then you have to implement additional logic to to control above signals using clock signal. Please see switching waveform given in datasheet (page 8) for more information.
Thanks and Regards,