The following itinerary is actually not a suggestion - as mentioned the department of conservation requires you to hike the trail in 4 days and you've to stay in the mentioned huts.

Day 1: Glade wharf - Clinton hut
(~1 hour)

Start point

Well, the first day is a lazy one. It takes longer to get to the starting point of the track than from here to the first hut. There's no direct access to the trail head - you have to take the hiker ferry from TeAnau Downs. From the wharf it is merely a hour to the Clinton hut (and even less to the hut of the guided walks). After crossing the river via a swing-bridge the track follows the left side of the deeply forested valley.

Day 2: Clinton hut - Mintaro hut
(~5 hours)

Waterfallmania

Just like the day before you continue to hike upstream of the Clinton River. At the time we hike the trail there were heavy rainfalls and the river actually flooded the trail so it was a fairly wet experience here. However, don't consider rainfalls as something bad per se because once the track leaves the deep beech forest the scenery welcomes you with a zillion waterfalls. In sunny conditions you should be able to spot the Mackinnon Pass and the Pompolona ice field. The Mintaro Hut is situated just below the pass.

Day 3: Mintaro hut - Dumpling hut
(~5 hours)

Mackinnon Pass

Today is the most strenuous part of the track although not all that difficult. In the morning you've to hike several switch back up to the Mackinnon Pass, the highest point of the track. The pass offers great vistas of the valley systems. From here it's all downwards, partially over boardwalks. Don't miss the 1h detour to the Sutherland Falls - one of the highest waterfalls of the planet! From the trail crossing it only an hour to the Dumpling hut.

Day 4: Dumpling hut - Sandfly point
(~4-5 hours)

The finish line ...

On the final day you have to take care of your timing because the ferry leaves at 2pm at Sandfly point and there's no overnight option at the wharf. It's a fairly easy walk but it's 18km long. From Dumpling hut you follow wild Arthur River downstream. This is an interesting big rock section with several river chasms, cascades and waterfalls. The 20min ferry trip back to civilization provides the first dramatic views of Milford Sound (and it's definitely worth to take a boat trip out into the Sound from here).