when it all makes sense?

Depends on your boss.  Some may hand stuff over to you sooner, and some may never hand you anything at all.  Does your boss like you, which is different than respecting you.  You won’t be able to answer that question until you have put in a good year or so, as each person has a different personality.  I learned a lot about planning from a landscape architect.  He didn’t like me personally, and I don’t think he took urban planning seriously.  Looking back I should have left after I put in a year, rather than sticking around to sit for the AICP exam. 

Since you work in such a small company you will probably have more of an opportunity to learn things hands-on than if you were working for a company that is only slightly larger (20-30).  You are probably scratching to do actual design work and take charge of client contracts.  Give it time.  I would say at least 1-2 years.  Finally, people’s personalities don’t change much, and the same goes for employers.  If you reach a road block in terms of growth and responsibilities look for work at another firm.  If you really want to consider going into business yourself, start small with independent contract work as side jobs.  

Given that you are working for a residential landscape LA firm, you will probably get to do some construction administration out in field.  That is where you will start to see what you have detailed become reality and will have a better understanding of what it was you have drawn in 2D.  When it really starts to make sense is when/if the contractor has an issue and you have to talk them through it or work out the design/construction collaborating with them.  When you successfully manuever your way through one of those discussion you will gain confidence that you really do know what you are doing and the next time you need to detail something you can pull from this experience and move forward. 

I have also found through out my career that establishing a close working relationship with contractors can also be helpful.  Bounce your questions off of them too.  Since they are the ones  that have to build the designs you are creating.  It ends up being a win win in the end.

Best advice I ever received: Your job is to work with, not just for, your client. That applies to the person who hires you to design something and the contractors who are hired to implement it.

Another good piece of advice: Keep copious notes and take lots of pictures. Then take a few more pictures.

Finally: Be alert, watch where you walk, and don’t trip over the stringline.

When you’re on a job site, if something doesn’t look like you think it should, don’t be afraid to point it out and find out why the contractor did what they did. Maybe they missed something on the plan and it’s been built wrong; maybe it’s not finished; maybe you missed something when you drew/specified it. If you’re not sure, it’s okay to call back to the office to talk to your boss.

If you know who the contractor is before you get on site that would be great.  Walking onto a job site and seeing a familiar face always helps to put one at ease.  Call ahead let them know you are coming out to the job to observe the construction and answser any questions they may have.  Be confident but not arrogant.  If this is the initial meeting on site before construction then its a clean slate and you are basically just going to introduce yourself and see if they have any questions before the shovel goes in the ground.  Like others have said if you aren’t sure of an answer don’t just wing it, call the boss or designer and ask them.  The work crews are usually cool unless you give them grief.  Sometimes it is necessary to give them grief, but don’t start off your relationship that way.  Contractors can also be a good resource for solving a problem encountered in the field, so make sure you listen and don’t dismiss their ideas.  Building a strong working relationship is key.  That way future site visits will be pleasant and they will look forward to you coming onsite.