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There are no hard and fast rules when it comes to fingering, but those who use "standard" fingering positions say it's easier to remember the melodies.

Playing a Five String Kantele

Rest your palms on the upper corners of your instrument.

Use your right hand thumb to pluck the shortest string - #5 - by moving your thumb away from you, "down and across the string."

Use the index finger of your left hand to pluck the next string (#4) by moving the pad of your finger across the string towards your body.

The middle finger of your left hand plucks the middle string (#3) the same way.

The ring finger of your left hand plucks the 2nd string of the kantele.

The index finger of your right hand plucks string #1 -- the longest string. Some players use the middle finger instead.

string #1 - D - right hand index finger
string #2 - E - left hand ring finger
string #3 - F# - left hand middle finger
string #4 - G - left hand index finger
string #5 - A - right hand thumb

Playing a Ten String Kantele

Finger positions for a ten string kantele

The ten string kantele is fingered the same way as the five string except that the right hand thumb also plays the two top (shortest) strings, your right hand index finger will pluck the third longest string, and the middle finger of your right hand will pluck the two bottom (longest) strings. Here is a finger chart for a kantele tuned to D Major (string #1) is the longest string:

string #1 - A - right hand middle finger
string #2 - B - right hand middle finger
string #3 - C# - right hand index finger
string #4 - D - right hand index finger
string #5 - E - left hand ring finger
string #6 - F# - left hand middle finger
string #7 - G - left hand index finger
string #8 - A - right hand thumb
string #9 - B - right hand thumb
string #10 - D - right hand thumb