This little piece is excellent training for the left hand in approaching the dreaded B flat chord. Most beginners have two problems with this chord: one is the big stretch between the 1st and 6th courses, which usually has to be managed by the 3rd and 4th fingers; the other is recognizing when they've got it right, because a shortfall in either direction produces a consonant chord. This piece doesn't use the full B flat chord, but it does require most of the lesser combinations which build up to it, so is useful practice for judging spacing, and gradually building up the stretch between your 3rd and 4th fingers.
The critical first step is to plant the 3rd finger perfectly for the opening note; the hand will probably need to be a little further forward for these B flat chords shapes than you might expect. The finger must be right up to (but not on) the fret, relaxed and gently curved at each joint, not locked straight with tension. If this finger is locked straight the other fingers - especially the 4th - have little hope of moving well around it. With the 3rd finger thus planted, locate the 3rd and 2nd course notes at the same fret, which your 4th finger will need to play in the opening two bars. Move the 4th finger back and forth between these notes to get a feel for the different stretches, then try the notes in context. The 4th finger will need to bend more for the 2nd course note than for the 3rd course. Note that the 3rd finger should remain planted for the whole of the first 5 bars. At the end of bar 1, lift the 4th finger promptly so that the open 2nd course at the beginning of bar 2 is not marred by hangover resonance. Don't lift the 4th finger too far from the strings; it will need to find its way to the 2nd course very soon.
Another little location problem concerns the 1st finger on the 1st fret during the first 4 bars; it needs to move back and forth between the 3rd and 2nd courses, and it will also need to be more tightly bent for the 2nd course note than for the 3rd. Use the anchored 3rd finger as a reference point to help you gauge the stretches required, and try alternating the 1st finger notes before attempting them in context.
In the second line, the 3rd finger moves to a 5th course anchoring point, still at the 3rd fret. You can bend the finger just a little more for this note than its 6th course predecessor. Lift the finger at the end of bar 10, so the note doesn't continue to sound beyond its usefulness. Note that you will have to lift this finger whilst simultaneously locating the 3rd fret on the 2nd course with your 4th finger. You can start to plan for the fingering of bar 11 whilst you're playing bars 9 and 10, because your left hand doesn't need to move during those bars. This sort of thinking ahead is really useful for handling complex fingering changes.
As a final point, the 4th finger is usually the smallest finger, and the one which has most difficulty in stopping a double course cleanly, especially when it has to be somewhat tucked in beneath the 3rd finger. Take care that every note sounds cleanly; if it doesn't, check your 3rd finger anchorage again to make sure you have positioned the hand well for the stretches. If you can negotiate this piece cleanly and without fumbles, you're well on your way to the full B flat chord.