Always collect the information about a document at the same time you download the image. You can't be sure that the collection will be online if you go back to look at it later -- over time, commercial websites may lose the right to host the database.
Without the information that identifies the image and where it came from, you can't evaluate the document properly or evaluate completely the information it contains.
In her book Evidence Explained (page 8 of the 3rd revised edition), Elizabeth Shown Mills emphasizes how important this is. She says:
Consulting maps and gazetteers from the period of your document can also help in your analysis. Hudson City, New Jersey is now part of Jersey City, in Hudson County, directly across the Hudson River from Manhattan.
Identify the document
The item you posted is an abstract from a muster roll.
On Fold3, the information about the record is below the image viewer.
The Source information includes the following:
Publication Title: New York, Civil War Muster Roll Abstracts, 1861-1900
Content Source: New York State Archives
Fold3 Publication Year: 2014
Short Description: Abstracts from original muster rolls for
New York State infantry units involved in the Civil War. 1861-1900
The main page on fold3 for this collection says:
The records have personal enlistment information and military service,
as well as regiment engagements. The personal record and unit
information makes the collection valuable to anyone with New York
ancestors in the Civil War era. The beginning of each regiment record
has information on the regiment including the commanding officers. In
a few of the abstracts, a detailed history of the unit also appears.
The regiment's information will have to be browsed for or searched by
regiment.
Gather information from the repository that holds the record
The New York State Archives' page on Civil War Service Abstracts says:
Abstracts of muster rolls of NYS Volunteer Units that served during
the Civil War (Series 13775) are available on self-service microfilm.
The Archives does NOT have original muster rolls.
Content varies, but abstracts generally provide: enlistment date; age;
place of enlistment and for how long; date mustered in; grade;
company; regiment; date left organization; reason for leaving (killed,
discharged, deserted, etc.); in what grade; and "remarks."
"Remarks" may or may not include service details (reduced to private,
deserted, temporarily assigned to special duty, etc.). Sometimes, but
not always, physical descriptors (height, eye color) are present.
Names of soldiers’ parents or spouses are not present.
Offsite researchers may print out and mail in a War Service Records
Request Form to purchase a photocopy of an abstract.
Note that the New York State Archives doesn't have the original muster rolls from which this information was abstracted. You will have to locate other sources about the New York State Volunteers in different repositories to get more information.
Where to find more information
These abstracts are also available on Ancestry, in their database New York, Civil War Muster Roll Abstracts, 1861-1900. Without a subscription, you can still read the About the Database information on the main search page for the database, and get some clues about how the records are arranged by looking at the drop-down menus to the right of the search box, underneath where it says Browse this collection.
The image shown for Adolf Neumann can be viewed here: shareable link. Ancestry's sharing feature does not allow users to share the abstracted information from the record page. The record page says:
Name: Adolf Neumann
Age: 38
Birth Year: abt 1823
Enlistment Year: 1861
Enlistment Location: Hudson City, New Jersey
Muster Year: 1861
Separation Details: Discharged
Source Citation
New York State Archives, Cultural Education Center, Albany, New
York; New York Civil War Muster Roll Abstracts, 1861-1900;
Archive Collection #: 13775-83; Box #: 208; Roll #: 1075-1076
Source Information
Ancestry.com. New York, Civil War Muster Roll Abstracts, 1861-1900
[database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc.,
2011.
Original data: Civil War Muster Roll Abstracts of New York State
Volunteers, United States Sharpshooters, and United States Colored
Troops [ca. 1861-1900]. Microfilm, 1185 rolls. New York State
Archives, Albany, New York.
Further research will be required before you can locate medical records about this soldier, since this record gives you no help -- there is no hospital name or date the soldier was admitted. Medical records are not likely to be online, and they are likely to be arranged by medical facility and arranged chronologically. For more information, see Reference Information Paper 109, Military Service Records at the National Archives.