A favorite activity of many lunar observers is to challenge themselves to observe really "young" or "old" crescent Moons. A razor thin crescent Moon can be an inspiring sight. Lunar Calculator can help you decide when to try for a "personal best" or when to alert your club for a young or old Moon, by creating a list tailored to your criteria.
The conditions have to be just right. Of course you will require an unobstructed horizon and a clear an atmosphere as possible. More importantly, you need the Moon to cooperate. If the Sun is just setting at new Moon, you won't see a crescent for another 24 hours. On the other hand, if the Moon is younger than 10 hours, the sky will be too bright. Wait for the sky to darken, and the Moon sets; try too early and the sky is too bright.
Generally, the best time for evening crescents is in early February-March (September-October) for the northern (southern) hemisphere. The best time for morning crescents is in September-October (February-March) for the northern (southern) hemisphere.
Here's an example with the Sun at an altitude of -6.8 degrees. The thin crescent here is 3.0 degrees above the horizon, just to the left of the tallest building on the left. Mercury is at the top. This particular crescent is not that young: 34h19m.


Now you can see why you need to plan! Launch the crescent search through the utilities menu:
to get the crescent search window. By default it shows the evening "Month by Month" data, with the upcoming new Moon (unless it happened within the last 48 hours):

You can skip back and forth and jump from one month to the next by clicking on the appropriate button. To change from evening to morning, click on the menu and choose morning:
and the program will switch.
Solar altitude is the height above the horizon of the Sun. In this case, it is -6.5 degrees, which is a good starting number. You may find a slightly different number better suits your needs. -8.0 will make the sky darker, but it also means that a young Moon will be closer to the horizon, or even below it.
Elong is the elongation in degrees from the Sun to the Moon as viewed from your observation point. The geocentric value is typically less than a degree different.
Illum is the % illumination.
Click on the "Search" tab, and you will see this window:
The normal Windows ctrl-C function will copy the click-and-drag selection to the clipboard so you can paste the output into any other program that accepts text from the clipboard (Word, Wordpad, Notepad, etc.)
Maximum age and Minimum lunar altitude are used to filter out those cases which do not meet your search criteria. For example, if you want to show only those cases where the Moon is less than 20 hours, put 20 in the box. The minimum lunar altitude is useful to eliminate cases where the Moon is below the horizon (0.0), or any higher local horizon you may have. You can enter a negative value if you are interested in seeing if it's only just below, or you are observing from a mountain top which permits you to have a horizon below 0.0 degrees.
Objects near the horizon are affected considerably by atmospheric refraction. According to Meeus, a star on the geometric horizon will be lifted on average 34', just over a lunar diameter. For the above tables, Lunar Calculator uses the formula from Astronomical Algorithms to calculate the refraction component as a function of geometric altitude, but it does not take into account seasonal or temperature differences. Meeus notes that daily fluctuations of 0.3 degrees do occur, and can even be larger, so it makes no sense to expect high accuracy from any refraction calculation.
Because the age and altitude of the Moon and solar altitude depend critically on the observer's longitude, the results from this table apply only to your local area. Every degree of longitude changes the time by about 4 minutes.
In the case of observers at higher latitudes, it is possible for the Sun to never go below the "Solar altitude" during the summer months. When this happens, instead of a date with alt/az numbers, you will simply see a message like "Solar altitude never crosses below -7.0" (except with the actual value you decide to use).
The time of year plays a role in young/old Moon visibility is the angle the ecliptic makes with the horizon. For example, in late summer in the northern hemisphere, the ecliptic makes a shallow angle to the horizon, so a young Moon will be lost in the horizon glow. In contrast, in spring, the ecliptic stands almost upright so a Moon of a given age will be higher in a darker sky, and therefore easier to see.
The youngest crescents you will ever see will fall very close to lunar perigee. The reason is that at this time, the Moon is moving fastest in its orbit, and so will have a greater elongation from the Sun for every hour of age. The greater the elongation, the higher above the horizon it will be, all else equal.
The values you choose for "Maximum age" , "Solar altitude", "Minimum lunar altitude", will be stored in the config file when you exit Lunar Calculator.
Lite users can only go back and forth or search for 2 months.