Here’s my translation

Alan

Búi fór nú til þess er hann kom í hólminn. Var þar Kolfinnur fyrir og fjöldi
Búi now journeyed until (see under til, Z7) he came to the-islet. Kolfinnr was there before (him) and a great-number

manns því að forvitni mikil var mönnum að sjá atgang þessa ungu manna því að
of persons (men) (I would have expected „manna“, gen plural) because a great curiousity was with (the) persons (ie folk were very curious) to see (the) battle of these (masc gen pl agrees with „manna“) young persons (men) because

báðir voru þeir sterklegir.
they both were strong-looking.

Það var þá siður að kasta feldi undir fætur sér. Það voru lög þeirra að sá
That was then (ie at that time) (the) custom to throw (cast) cloaks under their feet. It was their law (neut plural) that that-one (he)

þeirra er af feldi hopaði skyldi leysa sig þrem mörkum silfurs. Sá þeirra
of them who moved-backwards (retreated) off (the) cloak should pay-out (absolve?, redeem?) himself with three marks of silver. That-one of them

var óvígur er fyrri lét sitt blóð á jörð.
was unable-to-fight (disabled, disqualified from fighting?) who sooner (ie first) let-(spill) his blood on (the) ground.

Eftir það voru sögð upp hólmgöngulög milli þeirra. Búi átti fyrr að höggva
After that were declared (the) rules-of-engagement-for-the duel between them. Búi was-entitled (eiga, Z4) to strike sooner (ie first)
(I am slightly more inclined to associate “milli þeirra” with the rules rather than the declaration/proclamation and that the rules proclaimed were those specific to this particular duel rather than the rules for all duels, albeit that the rules for this duel would be consistent with the standard rules of engagement.)

því að honum var á hólm skorað. Hvortveggi hafði góðan skjöld og öll önnur
because (lit:) (it) was challenged to him on (the) islet (ie he was the one who had been challenged to the duel). Each-of-the-two had a good shield and all other

vopn. Búi hjó þá til Kolfinns. Kolfinnur brá þá við skildinum og tók af
weapons. Búi hewed (struck) then at Kolfinnr. Kolfinnr warded-off (the blow) with the-shield (see bregða e-u við, Z7) and (the blow) took off (removed?, taka, Z12)

öðrumegin mundriða. Eftir það hjó Kolfinnur þvílíkt högg til Búa. Búi hjá (hjó) þá
(the) other-side of (the) shield-handle. After that Kolfinnr hewed (struck) a similar (such-like) blow at Búi. Búi hewed (struck) )(must be typo) then

til Kolfinns og gerði ónýtan fyrir honum skjöldinn og særði hann miklu sári
at Kolfinnr and rendered (made) the-shield useless (accusative) for (fyrir, Z3, or before, Z1, not clear which is intended) him and wounded him with a great wound

á höndina. Var Kolfinnur þegar óvígur. Menn hlupu þá í millum þeirra og voru þeir skildir.
on the-arm (singular). Kolfinnr was at-once unable-to-fight (disabled, disqualified, disarmed J). Persons (men) ran then between them and they were separated.

Eftir það fór hvor leið sína.
After that each went his-own way

Fór Kolfinnur á Korpúlfsstaði og batt Korpúlfur sár hans og kvað eigi minna
Kolfinnr went to Korpúlfsstaðir (Korpúlfr’s-steads) and Korpúlfr bound his wound(s) and declared (it) not less-than (minni, compar adj)

að von um skipti þeirra Búa. Dvaldist Kolfinnur nú þar um stund.
according to (the) expectation (as was to be expected, cf at vánum, under at, Z9 and under ván, Z1) concerning (the) fight (dispute) of them, Buí and he (ie Kolfinnr)). Kolfinnr now stayed there a while.

Búi sneri frá hólmstefnu heim til Kollafjarðar og var Ólöf við laug og
Búi turned (went, passed tense) from the meeting-on-(the)-islet (ie the duel) back (lit: home) to Kollafjörðr and Ólöf was at (the) hot-spring (singular, may be taking a bath?) and

heilsaði Búa.
greeted Búi.

Hann tók kveðju hennar og mælti: "Svo hefir nú borið til um fund okkarn Ólöf
He accepted her greeting and spoke “(It) has now happened (see bera til, Z.ii.3) concerning our fight (fundr, Z3), Ólöf,

að eg mun eigi einn saman fara til hellis míns. Þykir mér og leiðint að
(such) that I will not go one-alone (all by myself) to my cave. (It) seems to me also tiresome (leiðindr, CV) to

ganga hingað hvern dag til tals við þig. Muntu nú fara með mér að sinni."
walk hither each day for conversation with you (presumably just the walking part is tiresome). You will now go with me for the present.”

Ólöf segir: "Það mun föður mínum illa hugna."
Ólöf says: “That will be ill-pleasing to my father.”

Búi segir: "Hann mun nú ekki að spurður."
Búi says: “He will now not be-informed (past part of spyrja as adj) of (it).”

Tók hann þá Ólöfu upp á handlegg sér og gekk leið sína. Fóru þau þar til er
He took then Ólöf up in his arm and (he) went (on foot) his way. They went until

þau komu í helli Búa.
they came to Búi’s cave.

Var Esja þar fyrir og heilsaði þeim: "Þykir mér þú Búi nú haft hafa vel að
Esja was there before (them) and greeted them: “Búi, you seem to me now to have done (fared, hafa, Z10) well in

máli, varið hana Ólöfu fyrir vanmennum enda flutt hana nú úr klandri þeirra.
(the) matter, (have) defended (verja, Z1) her, Ólöf, before (in the face of) worthless-persons (men) and-moreover conveyed her now out-of (away from) their molestation (grubby paws).

Skaltu Ólöf mín vera hér velkomin."
Ólöf mine, you shall be welcome here.”

Ólöf kvað nú Búa mundu ráða sínum vistum að sinni.
Ólöf declared now Búi would govern (dictate, ráða, Z7 or Z8) her food-and-lodgings for the present.

Kolfinnur spurði brotttöku Ólafar.
Kolfinnr was-informed of Ólöf’s kidnapping (lit: away-taking, removal, noun).