For warmup, I find that hitting ~ 30 balls on range followed by chipping, then putting works.  On the range, it depends on what course I am playing, but primarily it is a combination of 10 balls with one of my wedges, 10 balls with mid-iron, 10 balls with driver--I always finish with a few balls that simulate the opening tee shot.  Basically try to mentally create the opening shots that I will need to hit to walk off with the intended score.

after some general warm up and stretching I like to start with putting and chipping just to get a feel for the speed of the greens.  then I progress to full shots.  I make sure to hit some fades, draws, high and low etc.  some days it seems that I'm having more trouble with certain shots.  don't fight it.  I play my best golf when I accept the shot shape I am hitting naturally rather than the one I want to make.  from there I start to practice some of the shots that I'm likely to have on that particular course always ending with the shot for the first tee.

Is your slow start due to a poor opening tee shot?  Bad putting?  No real pattern?

WW

Hey, Jack!  Great question.  My humble opinion, make this part of your routine.  Whatever that is.  Just like your swing and your life. Make it yours.  All yours.  Only yours.  Whatever you do, make this part of your round, because in reality, it is.  Warm up, your game and warm down is all part of the thing called, "JACK'S GAME."  Good luck, Jack!  

Jack,

   I used to struggle with this same issue and then I made a change that has really helped me mentally and physically prepared for each and every round.  I am of the mindset that I like to get to the golf course very early.  I usually like to be at the course no later than one hour before my round.  For me an hour and a half prior to my round is ideal.  When I get there, I go in an pay and then my preparation process begins.

  First, I get my supplies out of my golf bag and into my cart, tees, ball marker and divot tool in my pocket and glove in back pocket.  I like to make sure my cart is ready so that, in the event they try to get me out early, I am not fumbling around trying to do all of these things at the first tee.  Then, I like to study the score card a bit if I haven't done so already the night before.  I look at what tee box I will most likely play and look at the yardages for each hole.  Based on those yardages, I will decide on what clubs am I most likely to hit that day and take them with me to the range.  

  Before hitting any balls, I like to stretch, a lot.  I stretch my hamstrings to take pressure off of my lower back, my hips, quads and then spend a lot of time stretching my back with various exercises.  Then I will swing a club or two to loosen up my shoulders.  Once I am loose, I walk over to the chipping area and chip for about 5-10 minutes before hitting any full shots.  It helps my rhythm and confidence and gets me even looser.  Once I am done chipping, I will go up to the range with the clubs that I selected based on the score card/yardages and hit those.  

  Make that practice meaningful.  Check your loft and launch angle.  Only you know how you typically hit the ball.  Aim at yardage markers or flags and treat them as if you are making your approach to that flag with that one ball you are about to it.  This helps me mentally prepare for the round.  Don't make a mistake by over hitting your driver.  I hit 4 maybe 5 drives on the range unless my driver is wayward then I might hit a few more.  I save the last 10 balls for my driver just in case I need to make an adjustment with my driver.  If I hit the 4-5 balls the way I should, I use the last 5-6 balls for a "practice" hole.  I will tee one up and hit my driver.  Then, based on that drive, straight, fade or draw, I will hit a different club up until the last ball I hit an "approach" shot with a wedge.  

   After that, I am mentally prepared from that wedge shot I just hit, I have already chipped, I will spend sometime on the putting green and then I am ready to go.  When I putt, I pick ONE hole and putt from various lengths and angles to that one hole.  Spend more time putting from distances you typically have and struggle with.  

   At that point, it's time to play and I am mentally and physically ready.  I hope that helps!  Hit them straight my friend.  

Greg

There really isn't much else you can do differently unless you want to go to great depths of preparation. By this I mean, maintaining your diet, pre-round stretches, any type of internal psychology you need to do to play well. All and all, it's your game and the way you think you need to prepare for it is all that matters to you. 

I'm a standard small bucket to get the feel and make sure I'm hitting the shots close to what I should on the course, and a good 10-15 minute putt session with a few chips here and there. 

Jack,

I've struggled having doubts about warming up the right way. Truth be told, everyone is different. I would recommend trying different types of routines n go with the one that you think allows you to be your best. For me, chipping first. Putting. 15 minutes on the range. Finish the range session with how your going to play the first two holes. It helps get more mind relaxed n not so anxious on those first couple shots. Hope it helps my friend. Play well. 

I try and follow a set routine.  Lag putts to get the feel of the green, a dozen or so 3-5 footers, over  to the range w/ sw, 8, 4, Driver.

Will hit the sw until i feel loose. 6 8-irons, 6  4-irons, 6 Drivers. and finish with 6 1/2 pitch shots.  Back to the putting green and hit 10-12 chips and off to the first tee.  Use to hit a lot more but as I mature in life I do not want to get tired before I play or wear out around 16.

I have saw many pros hit shots in sequence like they were playing a hole. Like tee shot, followed by approach in to the green. I tried  it and I think it helps visualize your shot a lot better on the range.

For me, a little stretching is much more important than hitting balls on the range.  I might do a little putting to get a feel for the greens, but that's about it.  I have two very young kids, so my golf time is very limited.  Showing up an hour or more before a round is just not realistic.  However, I have found I don't do any worse by just showing up and playing as long as I have my mind right and my body loose.

Usually a 6 pack and a few shots of Jack warms me up pretty good.. j/k... 

Like Tdogg, I have 2 young boys so it's tough to get out let alone getting there early to warm up..   My goal is to try and show up a 1/2 hour before tee time, i hate rushing..   First thing i'll do is stretch for at least 10 minutes..  Whatever time I have left, I'll try to hit a small bucket if there's a range at the course, chip around and then putt a few..  I like to give myself 5 minutes before tee time to relax and get ready for a fun day...  

 To me, the most important part of my warm up routine is stretching out...  It' a must for me...  Getting old...

I like the warm-up routine I picked up from the Shed Pounds to Shave Strokes workout program developed by Christian Henning - helped me lose 20lbs btw. He's got some great workout routines that don't require a whole lot of equipment or even a gym membership. His warm-up routine is pretty simple too. It consists of a little foam rolling and plyometric exercises before reaching for any clubs. He recommends putting first and finishing with a driver in your hands since that is likely the first club you will use on most courses - makes sense.

Lots of great comments, thanks guys.  I wish more courses had a place to stretch and warm up.  I would like to ride an exercise bike for a few minutes to get the blood flowing and heart rate up.  Then a place to do some stretching where you are not on the range in full view.  The most I usually see from most others is a couple of swings with 2 clubs and then it's off to whack a few balls. Tour pros have a whole fitness trailer to do a complete warm up in. There are some good youtube videos on the topic.  Before my next round I will get there earlier and do some stretching and more chipping than I have in the past. Good luck everyone to playing well as we move out of the warm summer months.