I recently got a knife as a gift and after only using it two times it has started to rust, despite making sure to properly clean it and dry it after using it. There is also one large spot of black/blue discolouration on the back of the knife. Also I'm not sure if this helps but the branding on the knife says 'Okeya'. How can I avoid this happening and what should I do to treat the rust?
Just glancing at the knife, it appears to be made with rough san mai technique forged stock or a similar form. This is a technique were a soft iron or steal is sandwiched with a higher carbon hardenable steel center layer which is then honed and will hold an edge. The outer layer is left rough and somewhat decorative, and though it is soft and cheaper metal, it actually adds to the durability of the blade by being softer. However, it is porous and can tend to catch water, acids and corrosive items so could be prone to rusting if not sealed and yours obviously fits that description.
Vinegar as suggested, diluted, could well help clean off the rust, but be sure if you go that route to promptly clean any off and consider neutralizing it with a base such as baking soda. As light a layer as you have, just a good wash will likely remove it though. With any use of something like steel wool, keep it away from that beveled edge which should be you hardenable steel. I would tend to suggest a good wash and then not only dry it well, maybe even use some heat to make sure, such as a blow drier. Once good and dry, give it a light oiling as you would cast iron and keep it regularly oiled to keep a layer to prevent direct water contact.
Taking a look, I see Okeya knives listed as carbon steel and iron, never corrosion resistant. I would never soak, use a dish washer, or leave wet at all or in contact with anything corrosive such as fruit juice. If you use oil, light oil and flavor neutral, that will not go rancid.
A list of methods for removing rust from knives can be found at Knife Depot. In your case, as the rust appears very light and is recent, simply wiping with a vinegar cloth may be sufficient (possibly also needing a wipe with fine steel wool) and then wipe off any remaining vinegar.
In future, it is imperative that you dry the washed knife immediately and then apply a very thin coating of food safe (e.g., vegetable) oil (or fat) - wipe on then wipe off. Also, don't leave the knife wet (e.g., while using it) for any length of time - wipe with a dry cloth.
The rust is a common problem for carbon steel knives. I have two to Sabatier knives which are now more than 50 years old and have had some rust on them from time to time. I just clean them off with a Brillo pad or similar mild abrasive, dry them off and put them away (personally I would shy away from any "chemical solutions" (forgive the pun)). Over the course of the years, the blades have stained, but the, if it can be considered that, is cosmetic. What I do (or try to remember to do is to wipe the knive off after I take it out of the rack, just before I use it. (For the record, one of Sabatier's is a 12 inch vegetable slicer which is just as sharp now as it was 50 years ago.)