Here’s my translation

Alan

1. kafli - Frá Gnúpa-Bárði ok sonum hans
Chapter 1 – About Gnúpa-Bárðr (Bárðr of the Peaks) and his sons (plural).

Bárðr hét maðr, sonr Heyangrs-Bjarnar hersis úr Sogni.
(There) was a person (man) called Bárðr, son of Heyangrs-Björn, a local-chief out-of Sogn (District in Norway).

Hann fór út til Íslands í landnámatíð ok nam Bárðardal allan frá Kálfborgará til Svartár beggja vegna.
He journeyed out to Iceland in the-Period-of-Settlement (lit: Time of Land-Taking) and took (possession of) (nema) all Bárðardalr (Bárðr’s-Dale) from Kálfborgará (Calf-hillock´s-River) to Svartá (Black-River) on both sides.

Hann bjó at Lundarbrekku. Hans synir vóru þeir Þorsteinn ok Sigmundr, Nefsteinn ok Egill.
He lived at Lundarbrekka (Grove’s (lundr)-Slope). Those were his sons: Þorsteinn and Sigmundr, Nefsteinn and Egill.

Bárði þótti eigi viðra vel í dalnum ok eirði því ekki þar til lengdar.
(It) seemed to Bárðr (to be) not well of weather (viðri) (ie not a good climate) in the-dale and (it) did not spare (ease?) there for a long time.

Eitt vor sendi hann syni sína suðr yfir heiðar at forvitnast, hversu þar félli út veðráttufar. Var þat um gói.
One spring he sent his sons south over (the) heaths (plural) to enquire about how  (the) state-of-the-weather (wind) happened (lit: fell out) there. That was during Gói (Feb-March)

Kómu þeir aftr at hálfs mánaðar fresti ok létu vel af landi. Fundu þeir þá góubitla ok annan gróðr.
They came back after a half month´s delay and expressed approval (?) (cf láta vel yfir e-u) of (the) land. They found then rough-horsetail (From the context I think this must be Gói-beytlar, CV, a plant: equisetum vernum hyemale http://www.iceland-nh.net/plants/data/Equisetum-hyemale/equisetum_hyemale.html ) and other growth (ie vegetation).

Annat vor tók Bárðr sik upp með allan sinn varnað ok fór suðr Vonarskarð, þar nú heitir Bárðargata.
(The) next spring Bárðr took himself up and all his goods (household) and journeyed south (to) Vonarskarð (Mountain-Pass of Hopes?).

Hann nam síðan Fljótshverfi ok bjó at Gnúpi, ok var hann því Gnúpa-Bárðr kallaðr.
He took (possession of) Fljótshverfi (Lake´s cluster-of farms) after-that and lived at Gnúpr (Peak) and he was for-that (reason) (því) called Gnúpa-Bárðr (Bárðr of the Peaks).

En Egill, sonr Bárðar, bjó eftir at Lundarbrekku.
But (And) Egill, son of Bárðr, lived after at Lundarbrekka (Grove´s-Slope)

Hann átti Salgerði, dóttur Þóris snepils at Lundi. Þeirra sonr var Hrani hringr, sem því var kallaðr hringr,
He had (in marriage) Salgerðr, daughter of Þórir ‘flap’ of Lundr (The Grove). Their son was Hrani ‘Ring, who was-called ‘Ring’

at hann hafði rauðan hring á vinstri kinn. Hrani var snemma gerviligr ok inn mesti maðr.
because he had a read ring on (his) left cheek (of his face!). Hrani was soon accomplished and the greatest person (man).

2. kafli - Útkoma Helga króks ok landnám
Chapter 2 – (The) coming out (to Iceland) of Helgi ‘Hook’ and Settlement (lit: Land-Taking)

Maðr er nefndr Helgi krókr, sonr Goðlaugs Ásgeirssonar úr Sogni. Hann fór frá Suðreyjum til Íslands ok hélt skipi sínu í Skjálfandafljótsós.
(There) is a person (man) named Helgi ‘Hook’, son of Goðlaugr Ásgeirr’s-son out-of Sogn (District in Norway). He journeyed from the Hebrides, (Suðreyjar, lit: South Islands) to Iceland and steered (lit: held) his ship into Skjálfandafljótsóss (Quivering-River’s-Mouth).

Hann var skyldr Agli á Lundarbrekku ok Þorsteini í Reykjahlíð.
He was related to Egill in Lundarbrekka (Grove’s-Slope) and Þorsteinn in Reykjahlíð (Mountainside of Steam/Smoke).

Helgi reið frá skipi sínu at Lundarbrekku. Þeir feðgar tóku vel við honum, ok var hann þar um hríð.
Helgi rode from his ship to Lundarbrekka (Grove’s-Slope). They, father-and-son, received him well, and he was (stayed) there for a while.

Eitt sinn kom hann at máli við Egil, at hann vildi staðfestast þar í dalnum, en þá var allr Bárðardalr byggðr.
One time he came to speech with Egill, that he wanted to take-up-his-abode there in the-dale, but then (ie at that time) was all Bárðardalr (Bárðr’s-Dale) settled.

Egill mælti: "Hugat hefi ek at bólfestu hér fram til dala, ok er víða mjök byggiligt,
Egill spoke: “I have looked into a leasehold from here to (the) dale, and (it) is far-and-wide very habitable.

ok skaltu eiga land allt milli Skjálfandafljóts ok Mjóadalsár fram til Sanda."
and you-shall have all land between Skjálfandafljót (Quivering-River) ok Mjóadalsá (Slender-Dale’s River) forward to Sandar (The Sands, Sand-banks)

Eftir þetta riðu þeir Egill ok Helgi krókr at heiman ok skoðuðu landit ok kölluðu Króksdal fram með fljóti.
After this they, Egill and Helgi ‘Hook’ ride from-home and viewed the-land and claimed (cf kalla, Z4) Króksdalr (‘Hook’s-Dale) forward along (the) river.

Helgi reisti bæ á Króksdal ok kallaði Helgastaði. Hann átti konu þá, er Hallveig hét.
Helgi raised a farmstead in Króksdalr and called (it) Helgastaðir (Helgi’s-Steads). He had (in marriage) that woman, who was-called Hallveig.