I have the following reed switch sensor:
I need to connect this switch to counter input of this daq hardware.
The only info is the following:

How should I connect this to the counter-input? Any diagram would help. And do I need a debouncing filter?
The relevant information is in the manual. If you intend to count the reed switch transitions you will need a debouncing circuit as the 20MHz input capability will otherwise easily pick up each mechanical bounce.
The design will depend on the reed bounce time (typically around a ms), the Schmitt trigger hysteresis (not specified) and the maximum frequency you wish to count at. You may have to experiment a bit.
You can try something like a 1K resistor from the reed to +5 (other side grounded) a 4.7K series resistor to the input and a capacitor from the input to ground with a time constant in the 2ms range, so C ~= 0.002/5200, maybe try 470nF X7R or film.