The xview and yview methods of the canvas are used to scroll the canvas. These are the very same methods you use to connect scrollbars to a canvas. You can scroll by "units" or "pages". "units" is defined by the canvas options xscrollincrement and yscrollincrement.
The events you want to bind to are <Up>, <Down>, <Left> and <Right>.
Putting it together, you would create bindings that look something like this:
self.canvas.bind("<Left>",  lambda event: self.canvas.xview_scroll(-1, "units"))
self.canvas.bind("<Right>", lambda event: self.canvas.xview_scroll( 1, "units"))
self.canvas.bind("<Up>",    lambda event: self.canvas.yview_scroll(-1, "units"))
self.canvas.bind("<Down>",  lambda event: self.canvas.yview_scroll( 1, "units"))
You need to make sure the canvas has focus. You can explicitly give it focus, but you probably also want a mouse click to give focus to the canvas as well:
self.canvas.focus_set()
self.canvas.bind("<1>", lambda event: self.canvas.focus_set())
Here is a complete working example:
import Tkinter as tk
import random
class Example(tk.Frame):
    def __init__(self, parent):
        tk.Frame.__init__(self, parent)
        self.canvas = tk.Canvas(self, background="bisque")
        self.vsb = tk.Scrollbar(self, orient="vertical", command=self.canvas.yview)
        self.hsb = tk.Scrollbar(self, orient="horizontal", command=self.canvas.xview)
        self.canvas.configure(xscrollcommand=self.hsb.set, yscrollcommand=self.vsb.set)
        self.canvas.grid(row=0, column=0, sticky="nsew")
        self.vsb.grid(row=0, column=1, sticky="ns")
        self.hsb.grid(row=1, column=0, sticky="ew")
        self.grid_rowconfigure(0, weight=1)
        self.grid_columnconfigure(0, weight=1)
        for i in range(100):
            x = random.randint(0, 1000)
            y = random.randint(0, 1000)
            width = random.randint(10, 50)
            height = random.randint(10, 50)
            fill = random.choice(("red", "orange", "yellow", "green", "blue", "violet"))
            self.canvas.create_rectangle(x, y, x+width, y+height, fill=fill)
        self.canvas.configure(scrollregion = self.canvas.bbox("all"))
        self.canvas.bind("<1>",     lambda event: self.canvas.focus_set())
        self.canvas.bind("<Left>",  lambda event: self.canvas.xview_scroll(-1, "units"))
        self.canvas.bind("<Right>", lambda event: self.canvas.xview_scroll( 1, "units"))
        self.canvas.bind("<Up>",    lambda event: self.canvas.yview_scroll(-1, "units"))
        self.canvas.bind("<Down>",  lambda event: self.canvas.yview_scroll( 1, "units"))
        self.canvas.focus_set()
if __name__ == "__main__":
    root = tk.Tk()
    Example(root).pack(fill="both", expand=True)
    root.mainloop()