Here´s my translation.

Bolli tók vel undir þetta og bað Kjartan einn ráða þeirra máli.
Bolli agreed well -to this (ie readily fell into line with, took this on board,warmed to the idea, took it under his wing) and bade Kjartan alone to settle (ráða, Z9) (the) matter for them.

Viðræðu þeirra Kjartans hafði konungur fyrri spurt en borðin væru í brottu því að
(The) king had been informed of (the) conversation of them, Kjartan (and co) before the tables were (taken) away because

hann átti trúnað í hvers þeirra herbergi hinna heiðnu manna.
he kept (eiga, Z5) a confidence (confidant (?) in (the) quarters of each of them (?) of the heathen men (I don´t think I have the syntax quite right but I suspect this is close to the meaning.)

Konungur verður allglaður við þetta og mælti: "Sannað hefir Kjartan
(The) king became extremely-glad with this and spoke: “Kjartan has affirmed

orðskviðinn, að hátíðir eru til heilla bestar."
the-proverb, that festivals (high tides J) are best for luck (good omens, heill, noun, gen pl).” (All good things come to those who feast)

Og þegar um morguninn snemma er konungur gekk til kirkju mætti Kjartan honum
And forthwith next morning early when (the) king walked to church, Kjartan met him

á strætinu með mikilli sveit manna. Kjartan kvaddi konung með mikilli blíðu
in the-street with a great band of men. Kjartan greeted (the) king with great friendliness

og kvaðst eiga skyld erindi við hann. Konungur tók vel kveðju hans og kvaðst
and declared-of-himself to have pressing (not fastening J) (skyldr, Z3, acc neut pl) errands with him. (The) king took (received) his greeting well and declared-of-himself

hafa spurt af hið ljósasta um hans erindi "og mun þér þetta mál auðsótt."
to have been-informed of that, most-clearly, concerning his errand “and this matter will (be) for you easily-gained.”

Kjartan bað þá ekki dvala við að leita að vatninu og kvað þó mikils mundu við þurfa.
Kjartan bade them not to delay to seek for the-water and declared yet (it) would stand in need of much (note: genitive)(ie plenty of water would be needed).

Konungur svarar og brosti við: "Já Kjartan," segir hann, "eigi mundi okkur
(The) king answers and smiled with (that) (as was his want!): “Yes, Kjartan,” he says, “(there) would not for us

hér um harðfæri skilja þótt þú værir nokkuru kaupdýrri."
here be-differences (be-disagreement, see skilja, impers. Z5) because of (over, um, Z10) stubbornness  (ie we would not disagree with each other) even-if you were demanding-a- somewhat higher-price  (comparative) (driving a harder bargain).”

Síðan voru þeir Kjartan og Bolli skírðir og öll skipshöfn þeirra og fjöldi
After-that Kjartan and Bolli were baptised and all their ship’s-crew and a multitude

annarra manna. Þetta var annan dag jóla fyrir tíðir. Síðan bauð konungur
of other men. This was (the) second day of Jule (Christmas) before (the) divine-service (tíð, Z3). After-that (the) king invited

Kjartani í jólaboð sitt og svo Bolla frænda hans. Það er sögn flestra manna
Kartan to his Jule-banquet and also his kinsman Bolli. That is the word (saying) of most men

að Kjartan hafi þann dag gerst handgenginn Ólafi konungi er hann var færður
that Kjartan has, on that day, become submitted (become a retainer) to King Ólafr when he was conveyed (foera)

úr hvítavoðum og þeir Bolli báðir. Hallfreður var eigi skírður þann dag því
out-of (ie disrobed of) (the)white-(baptismal)-robes and they, Bolli (and he) both. Hallfreðr was not baptised that day because

að hann skildi það til að konungur sjálfur skyldi halda honum undir skírn.  
he stipulated (skilja e-t til, Z9) that, that (the) king himself should stand godfather to him.

Konungur lagði það til annan dag eftir.
(The) king committed to (?) that, the next day after.

Kjartan og Bolli voru með Ólafi konungi það er eftir var vetrarins.
Kjartan and Bolli were (stayed) with King Ólafr, (for) that which after was (ie remained) of the-winter.

Konungur mat Kjartan umfram alla menn fyrir sakir ættar sinnar og atgervi og er það
(The) king valued (meta) Kjartan beyond all persons (men) for reason of his ancestry and accomplishments and that is

alsagt að Kjartan væri þar svo vinsæll að hann átti sér engan öfundarmann
said-by-all that Kjartan was there so popular that he had for himself no enemy

innan hirðar. Var það og allra manna mál að engi hefði slíkur maður komið af
inside (the) court. That was (the) speech of all persons (men) that no such person (man) had come from

Íslandi sem Kjartan. Bolli var og hinn vaskasti maður og metinn vel af góðum
Iceland like Kjartan. Bolli was also the most-manly person (man) and well esteemed by good (morally commendable, honest)

mönnum. Líður nú vetur sjá. Og er vorar búast menn ferða sinna, svo hver sem ætlaði.
people (men) (just in case he was getting an inferiority complex J) Passes now this winter. And when Spring-springs (vára, verb) men (people) made-ready for their journeys, thus each (person) (hverr, not hvar) who intended (to travel)