How to Trench New Flexible Pipe or Wire Without Disturbing Existing Landscaping:
I recommend Funny Pipe (which is stronger than surface irrigation low pressure hose). There is also high pressure tubing that can be used if you want to put valves away from the house to distribute to several areas using valves. These can tolerate house pressure continuously.
To use this small size flexible tubing, you should plan on low precipitation rate emitters. Otherwise you have to use larger flexible tubing, which is more difficult to insert into the narrow trench.
If the flexible pipe is AFTER the valve, you can bury it 6-8" deep. If you are running high pressure tubing and putting the valves away from the house, you should plan to bury it deeper. This may require something more than a straight shovel to do the trenching.
Irrigation systems (valves) should be protected by a pressure regulator. So, the tap into the water supply should be made after the house's pressure regulator.