I have a shrimp net and have been shrimping many times.
I would say that a landing net probably won't be man enough for the job - you need a strong leading edge which is going to be pushed through the sand. Landing nets aren't made for that nor are they big enough.
But it is very easy to make your own shrimping net (I did) and you can easily find plans on the internet for them.
Here's the one I made:
Best time to go shrimping is outside the summer months. Now is a good time. Remember the old adage - only collect seafood if there's an 'r' in the month.
You want long, flat, sandy beaches.
I prefer to go shrimping as the tide is coming in. Go into the water up to knee depth (no need to go any deeper) then push the leading edge of the net into the sand so that it digs in the first couple of inches and with the net at about 45 degrees push it parallel with the beach. Keep going for some 20 or so yards and then haul up your net and see what's in there. Sometimes you get loads, sometimes you don't.
The idea is that the net disturbs the shrimp who are buried shallowly in the sand, and as they jump up they are caught in the net.
You'll get all sorts of other bits and bobs in the net as well - pay particular care and attention if there are any weaver fish because they can give you very nasty sting. For that reason always wear something on our feet (I go in with shorts and sandals regardless the time of year, but you can wear waders if you're made of weaker stuff).
Don't forget a bucket to put your catch in, tied about your waist if you're out netting alone.
And do keep an eye on the tide and make sure you move in with it.