कश्चित्कान्ता

कश्चित् कान्ताविरहगुरुणा स्वाधिकारात् प्रमत्तः
शापेनास्तङ्गमितमहिमा वर्षभोग्येण भर्तुः।
यक्षश्चक्रे जनकतनयास्नानपुण्योदकेषु
स्निग्धच्छायातरुषु वसतिं रामगिर्याश्रमेषु॥

This verse is basically telling a story or setting a scene. The first line alone is not a complete sentence and therefore will not give you a complete meaning. So let us turn to the अन्वयः to put this verse in prose format and hopefully make better sense of this. In order to do that let us first break apart internal and external sandhis.

कः-चित् कान्ता-विरह-गुरुणा स्व-अधिकारात् प्रमत्तः
शापेन अस्तं-गमित-महिमा वर्ष-भोग्येण भर्तुः।
यक्षः चक्रे जनक-तनया-स्नान-पुण्य-उदकेषु
स्निग्ध-छाया-तरुषु वसतिं रामगिरि-आश्रमेषु॥

This itself will probably give you a lot of clarity into the meaning. The translation is not at all difficult once you know the basic words. All you have to do next to reorder the words in a reasonable prose order. First let us find the simple core of the sentence. In Sanskrit the crux of any complete sentence is the verb. So we will find the verb: in the 3rd पाद, the second word is चक्रे. It is कृ-धातुः लिट्-लकारः प्रथमपुरुषः एकवचनम् (hence the meaning 'he/she/it did'. There are no other verbal forms in this verse so we will accept चक्रे as the crux of our sentence. Conveniently, the subject of the verb is the word right before it. Remember that a direct subject will be in प्रथमाविभक्तिः. यक्षः is in प्रथमाविभक्तिः, so we will accept it as being the subject of चक्रे.

So our sentence is: यक्षः चक्रे।

But there are three other प्रथमाविभक्तिः words in this verse. कश्चित्, प्रमत्तः and अस्तङ्गमितमहिमा, so why am I going with यक्षः? Let us see the meanings of each of these and it will be clear:

कश्चित् = some, someone
प्रमत्तः = distracted/deviate
अस्तम्-गमित-महिमा—
	अस्तम् गच्छति = to set, to wane/decline/decrease
	*यम्* अस्तम् *गमयति* सः अस्तङ्गमितः = that which is *made* to decline/wane/decrease → गम् + णिच् + क्त
	महिमा (महिमन्-शब्दः. The declension goes like महिमा महिमानौ महिमानः महिमानम् महिमानौ महिम्नः etc) = strength
	अस्तङ्गमितः महिमा *यस्य सः* अस्तङ्गमितमहिमा (षष्ठी-बहुव्रीहि-समासः) = *one whose* power was made to decrease

So you can see that all of these are actually adjectives for यक्षः (which is one of the types of supernatural being). So let us compose our sentence further:
कश्चित् प्रमत्तः यक्षः चक्रे। But the meaning of this is quite bare. 'Some deviated yaksha did.'

So the next order of business is to gather up all the same-vibhakti words in the sentence and group them together. This will give us more context as to the meaning of the sentence.
द्वितीयाविभक्तिः – वसतिम्
तृतीयाविभक्तिः – कान्ताविरहगुरुणा, शापेन, वर्षभोग्येण
पञ्चमीविभक्तिः – स्वाधिकारात्
षष्ठीविभक्तः – भर्तुः
सप्तमीविभक्तिः – जनकतनयास्नानपुण्योदकेषु, स्निग्धच्छायातरुषु, रामगिर्याश्रमेषु

Let us go through the meanings one-by-one.

वसतिम् – वसतिः means residence. वसतिं करोति means to take up residence (to make one's residence). Luckily we have कृ-धातुः here in the form of चक्रे, so the core of our sentence changes to यक्षः वसतिं चक्रे = a yaksha took up residence.
कान्ताविरहगुरुणा–
	कान्तया विरहः इति कान्ताविरहः = separation from a lover
		कान्ताविरहेण/कान्ताविरहात् गुरुः इति कान्ताविरहगुरुः
			तेन इति कान्ताविरहगुरुणा = great/grievous due to separation from one's lover
शापेन = by a curse
वर्षभोग्येण
	वर्षं भोग्यः इति वर्षभोग्यः = to be borne for one year
स्वाधिकारात् – स्वस्य अधिकारात् = away from one's duties. This is next to प्रमत्तः and therefore should be read with प्रमत्तः (distracted/deviated from one's duties)
भर्तुः – master's/leader's (Kubera is the master of all yakshas)
जनकतनयास्नानपुण्योदकेषु
	जनकस्य तनया इति जनकतनया
		तस्याः स्नानम् जनकतनयास्नानम्
			तस्मात् पुण्यम् जनकतनयास्नानपुण्यम्
				तादृशानि उदकानि जनकतनयास्नानपुण्योदकानि
					तेषु इति जनकतनयास्नानपुण्योदकेषु = at/by the waters made holy by the bath taken by Janaka's daughter
स्निग्धच्छायातरुषु
	छायया प्रधानाः तरवः इति छायातरवः = trees characterised by shade
	(↑this is a special समास called मध्यमपदलोपी, meaning that the middle word gets deleted)
		स्निग्धाः छायातरवः इति स्निग्धच्छायातरवः
			तेषु इति स्निग्धच्छायातरुषु = among the tightly packed trees characterised by shade
रामगिर्याश्रमेषु
	रामगिरौ आश्रमाः इति रामगिर्याश्रमाः
		तेषु इति रामगिर्याश्रमेषु = in the ashramas on Ramagiri mountain

Now that we know the meanings of each word, let us organise our sentence.
यक्षः वसतिं चक्रे।  What kind of yaksha?
कश्चित् स्वाधिकारात्प्रमत्तः अस्तङ्गमितमहिमा यक्षः वसतिं चक्रे। Why is his power made to decline?
कश्चित् स्वाधिकारात्प्रमत्तः भर्तुः शापेन अस्तङ्गमितमहिमा यक्षः वसतिं चक्रे। What kind of curse?
कश्चित् स्वाधिकारात्प्रमत्तः भर्तुः वर्षभोग्येन कान्ताविरहगुरुणा शापेन अस्तङ्गमितमहिमा यक्षः वसतिं चक्रे। Where did he take up residence?
कश्चित् स्वाधिकारात्प्रमत्तः भर्तुः वर्षभोग्येन कान्ताविरहगुरुणा शापेन अस्तङ्गमितमहिमा यक्षः जनकतनयास्नानपुण्योदकेषु स्निग्धच्छायातरुषु रामगिर्याश्रमेषु वसतिं चक्रे।
And there you have it. Our final sentence and the translation of this verse is:

कश्चित् स्वाधिकारात्प्रमत्तः भर्तुः वर्षभोग्येन कान्ताविरहगुरुणा शापेन अस्तङ्गमितमहिमा यक्षः जनकतनयास्नानपुण्योदकेषु स्निग्धच्छायातरुषु रामगिर्याश्रमेषु वसतिं चक्रे।
Some Yaksha, who was distracted from his duties, whose power was reduced by his master's curse that was to be borne for one year and that was grievous due to separation from his lover, took up residence in the Ramagiri ashramas, at the waters made holy by the bath of Janaka's daughter, among tightly packed shade-giving trees.
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Advanced topic for extra credit:
the meter that this verse is set to is called मन्दाक्रान्ता. It's called that because the beginning and end are both slow (मन्दा), and in between the pace picks up (आक्रान्ता).
The लक्षणसूत्र of मन्दाक्रान्ता is 'मन्दाक्रान्ता जलधिषडगैर्म्भौ नतौ ताद्गुरू चेत्'.
The syllables are organised as म्-भ्-न्-त्-त्-गुरु-गुरु. Using यमाताराजभानसलगम्, we can expand the syllable structure as:
- - - | - u u | u u u | - - u | - - u | - -   [u = लघु syllable, - = गुरु syllable]
The यतिs/pauses are shown by the लक्षणसूत्रम्–
जलधि = ocean; four oceans → 4
षट् = six → 6
अग = mountain, referring to the seven कुलपर्वत → 7
This means the syllables are grouped as first 4, second 6 and third 7.
The pauses are between each set. So we can deduce that there are two pauses. One between the first and second set, one between the second and third set.
- - - | -, u u | u u u | -, - u | - - u | - -   [, = यति]

Fun fact, the लक्षणसूत्रम् of the meter is in the same meter itself.
मन् दाक् रान् ता ज ल धि ष ड गैर्म् भौ न तौ तो गु रू चेत्
-   -   -  -, u u  u u u  -, -  u -  -  u -  -

Let us see how the verse fits into the meter.
कश् चित् कान् ता वि र ह गु रु णास् वा धि का रात्प् र मत् तः
-   -   -   -, u u u u u -,   - u  -  -   u -   -
शा पे नास् तङ् ग मि त म हि मा वर् ष भोग् ये न भर् तुः
-  - -   -, u  u u  u u  -, - u  -   - u -  -
यक् षश् चक् रे  ज न क त न यास् ना न पुण् यो द के षु
-   -   -  -, u u u  u u -,  -  u -   - u  - -
स्निग् धच् छा या  त रु षु व स तिम् रा म गिर् याश् र मे षु
-    -   -  -, u u  u u u -,  -  u -   -  u -  -

You can see the pattern is the same in all 4 पादs of the verse.