Arduino How to improve laser detection on photodiode?
How can I increasy sensitivity of the photodiode 


Sensitivity is usually not really a function of the photodiode but of the receiver circuit after the photodiode. One effect of the photodiode itself is that using a smaller photodiode will reduce its capacitance which might allow you to use a more sensitive receiver circuit.

Note: Sensitivity means the smallest signal an optical receiver can detect. Responsivity is photodiode characteristic giving the ratio between the optical input power and electrical output current. 

If you meant to ask about responsivity, for a photodiode, it's typically limited to 1 electron produced per photon received, so there is a maximum limit and you'll find many photodiodes approach this limit very closely. If you really need higher responsivity, you can consider using an avalanche photodiode but this requires a high-voltage driver circuit which is much more complex than what you have now.


  (and possibly reduce effect of daylight)?


You can add an optical filter in front of the photodiode to pass through your laser wavelength and block other wavelengths. 

Another typical trick is to modulate the laser at some frequency (often 40 kHz) and then add an electronic filter after the photodiode to specifically detect those signals. Off the shelf "IR" transmitters and receivers (like for the remote control of your TV) typically include the 40 kHz modulation and demodulation circuits.