Notice that lots of the language in the original document is place names. I’ll give you some terms to help wade through the rest and “translate” the first part for you.
Descendants of Gaardmand (type of farmer) Niels Uglsøe of Birk born circa 1754 and died 28 November 1826 in Humlegaard Birk, Gjellerup, Hammerum, Ringkøbing, Denmark, at the age of about 73 years, and he was buried 07 December 1826 in Gjellerup church graveyard, in Gjellerup [parish], in Hammerum [herred], in Ringkøbing [amt], Denmark.
Danish Census 1801
Ringkøbing, Hammerum, Gjellerup, 1801, 13, Birch
Niels Uldsøe age 48
Kirsten Knudsdatter age 45
Anders Nielsen 15
Knud Nielsen 11
Kirsten Nielsdatter 14
Else Nielsdatter 8
Christine Nielsdatter 6
Anders Bierregaard Widower 60, indsider/lodger
[my note: The children are named Nielsen and Nielsdatter after their father Niels.]
Niels was married with Hustru/Houswife Kirsten Knudsdatter of Birk. Kirsten was born circa 1756 and died in 1812 in Humlegaard Birk [gaard = farm], Gjellerup, Hammerum, Ringkøbing, Denmark.
The children of this marriage:
i Anders Nielsen blev født circa 1787 [was born circa 1787] in Birk…etc.
ii Kirsten Nielsdatter 1784-1805 age 21
iii Gaardmand/Farmer Knud Nielsen 1787 died 1875 etc. blev gift med [married with] Ellen Margrethe Pedersdatter first, and then with Kirsten Andersdatter.
iv Maren Nielsdatter 1790-1801
v Else Nielsdatter 1793
vi Kirsten Nielsdatter
vii Christiane Nielsdatter 1795
viii Kirstine Nielsdatter 1806
Niels was thereafter married with Ane Olsdatter circa 1827. Ane was born circa 1763 and died sometime after 1834.
Repeats the names of the above children and their birth information and mentions alternate names and alternate spellings of the names.
1834 Census for Kirsten Nielsdatter (child 2 - ii) with her husband Soren Sorensen Stoergaard and their children (substitute Danish o’s in there)
1834 Census for Knud Nielsen (child 3 - iii)
1840 Census for Knud shows that here he is enumerated with the name Knud Uglsøe.
More detailed marriage information for Knud and Ellen Margrethe Pedersdatter follows. She’s the daughter of Peder Rasmussen og/and Kirsten Nielsdatter. Knud and Ellen married 02 October 1816 i Gjellerup Kirke/in Gjellerup church, etc. Ellen blev født/was born 16 May 1796 in Meldgaard Birk…and døbt/baptized 16 May 1796 [that was fast - a typo, or there was a sense of urgency] in Gjellerup Kirke. She døde/died 30 July 1844 in Humlegaard Birk etc. og blev begravet/and was buried the 6 August 1844 in Gjellerup church graveyard.
Children of this marriage (Knud Nielsen Uglsøe and Ellen Margrethe Pedersdatter):
Kirsten Knudsdatter 1814 -1842
Niels Knudsen 1816-1819
Niels Knudsen 1819 (it was common to name a child after one who had died)
--Niels married Anne Sivebaek Sorensdatter on 30 April 1846
Ane Magrethe Knudsdatter 1822
Karen Knudsdatter 1825-1905. Karen blev gift med smed/blacksmith Christian Sorensen
Peder Christian Knudsen 1828
Kirsten Marie Knudsdatter 1831-1904 married Rogter Peder Jensen Bach and then Niels Jensen
Jens Knudsen 1834
Knud next married Kirsten Andersdatter on 16 October 1846. Kirsten blev født/was born circa 1798 in Bording, Hammerum, Ringkøbing, Denmark.
Back to Knud Nielsen’s siblings…Maren b 1790, Else b 1793, Christiane b 1795, Kirsten b 1806- gives their birth info again (given already, above) and alternate name spellings for them.
GENERATION 3 Children’s children / Grandchildren
I think you can follow who is descended from who down to this point:
Graestrup Church Book MARRIAGE RECORD
Knud Birch Nielsen, son of Farm owner Niels Knudsen in Burgaarde, Timring, born 24 March 1854, 29 years old - and the girl Servie Petrea Nielsen, daughter of the late farm owner Niels Nielsen Ballum in Dauding, born 15 November 1859, 23 years old. Marriage witnesses: the groom’s father and the bride’s brother
Married 30 March 1883 in church
Their fourth child (iv):
Niels Peder Knudsen Nielsen was born 09 December 1889 etc. died in Boise, Idaho, etc.
Married Wilma Robinson
To fill in what I didn't translate, you can copy and paste text into GramTrans, a free online translation tool. Mostly it's names, place names, dates, and key genealogy words (born, baptized, married, died, and job titles).
Of course any translation will give you the same proper nouns back (names of people and places).
I tried my best in the translation above. Disclaimer: I don't speak or read or write Danish! I have seen quite a few Danish family trees.
Hope this helps!