Description of the trek:

This beautiful trek crosses Egrisi mountains which separate Svaneti from Samegrelo lowlands. You will not come close to the highest mountains of Caucasus, but this small drawback is fully compensated by a very diverse environment. High passes with great views, magical lakes, rocky gorges, waterfalls, shepherds huts, remote valleys - this trek has everything. 

Or almost everything. There are no medieval stone villages, so typical for many Georgian regions. So, if you are coming for your first visit and have time for only one trek, I wouldn´t pick this one. It´s more suitable for people who have already seen the "highlights".

Duration: 4-5 days

If you are a swift walker, you can hike this trail in 4 days. Still, you should have at least one day as a buffer. Egrisi mountains are quite rainy because of the proximity of the Black Sea and it would be a pity if you walked so far and saw nothing because of the mist. In such a case, it's better to spend more time at the lake to get the best possible views.  
Also, you can save almost a day of timeif you hire a truck to take you all the way to the Natipuru hut. It´s probably even better this way as the Natipuru road is tough and not that interesting. For a transport, you will have to ask around Mukhuri village, the standard price of one-way ride these days is about 350 GEL. 

Diffculty: Hard

The trail is almost 80 km long from start to the end, crosses four mountain passes and several potentially risky water bodies. Especially the second half of the trek is quite remote and in case of any problems, it won't be easy to get any help.

When to go:

The best time is from the second half of July till the mid of September because of the most pleasant weather and lowest rainfall.
I would like to stress that my description is relevant to this "ideal" period. Overall, lakes are usually accessible from late June (when they are still frozen) till late September. I really don't recommend to try to visit them earlier or later - I am not saying it's impossible (nothing is "impossible"), but high passes will be covered by snow and crossing them could be tough and possibly life-threatening. I know several people who went there in late June and all, even though they are active climbers, admitted that it was just too risky and probably not a good idea. Also, during the late spring, lakes get quite a lot of rainfall.

Accommodation:

There are no villages or guesthouses where you could spend a night, you will have to pack everything necessary for a prolonged camping trip.

Alternative routes:

There are several alternative routes to the lakes. This post describes Mukhuri and Khaishi variants which are, in my opinion, the most scenic ones. The third, shorter route starts in Skuri.

How to get to Mukhuri:

The best place to start your trip is Zugdidi. Marshrutka to Mukhuri departs at 9 am. from the local bus station - it's the one by the bridge (42°30'31.9"N 41°52'09.0"E), not the one by the train station. The ride costs 3 GEL and takes more than two hours.
Another option is to take a taxi. Price for the ride to Mukhuri should be some 30-40 GEL (it's 40km) and the trip takes less than an hour.

How to Leave Khaishi:

Several marshrutkas heading either to Mestia or Zugdidi pass through Khaishi every day.