Write a program to display the previous and next day given a day of the week in C#

The problem with that approach is what happens when the user enters Monday or Sunday?
You need to use the user input to search your array for the entered day name. (Try a for loop)
If it isn't found, tell him that isn't a day and get him to try again.
if it is, then the loop variable is the index to "today".
To calculate the previous days index, add 6 to the index, and then use the modulus operator to take it back to a "proper" value. To calculate the next days, add one, and then use modulus again.

int prevIndex = (index + 6) % 7;
int nextIndex = (index + 1) % 7;

That works because the modulus gives you the remainder, and will always be between 0 and 6 inclusive. (So adding six and taking the modulus 7 effectively gives you a minus one that "wraps" round the end of the array!)

Hint: C# strings are case sensitive: so "Tuesday" will not match "tuesday": I'd compare them by converting them to lowercase before the actual comparison.

Member 14075859 wrote:

i gave up lol

Hey, don't give up!
Please, see this MSDN article: Performing arithmetic operations with dates and times | Microsoft Docs[^]
There's the most information you need to handle your problem.

Note: you can write a programme which operates on dates:

//needs reference to System.Globalization
CultureInfo ci = new CultureInfo("en-us");

DateTime givenDay = new DateTime(2019,01,01);
DateTime prevDay = givenDay.AddDays(-1);
DateTime nextDay = givenDay.AddDays(1);

Console.WriteLine("given day: {0} ({1})", givenDay.ToString("yyyy-MM-dd"), givenDay.ToString("dddd", ci));
Console.WriteLine("prev day: {0} ({1})", prevDay.ToString("yyyy-MM-dd"), prevDay.ToString("dddd", ci));
Console.WriteLine("next day: {0} ({1})", nextDay.ToString("yyyy-MM-dd"), nextDay.ToString("dddd", ci));

Result:

given day: 2019-01-01 (Tuesday)
prev day: 2018-12-31 (Monday)
next day: 2019-01-02 (Wednesday)

or on enums (Enumeration types - C# Programming Guide | Microsoft Docs[^]):

public enum WeekDays { Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday };

int givenDay = (int)WeekDays.Sunday; //(int)WeekDays.Tuesday;
int prevDay = givenDay-1;
if(prevDay<0) prevDay = (int)WeekDays.Saturday;
int nextDay = givenDay+1;
if(nextDay>6) nextDay = (int)WeekDays.Sunday;

Console.WriteLine("given day is: {0} (value of: {1})", Enum.GetName(typeof(WeekDays), givenDay), givenDay);
Console.WriteLine("prev day is: {0} (value of: {1})", Enum.GetName(typeof(WeekDays), prevDay), prevDay);
Console.WriteLine("next day is: {0} (value of: {1})", Enum.GetName(typeof(WeekDays), nextDay), nextDay);

Result:

given day is: Sunday (value of: 0)
prev day is: Saturday (value of: 6)
next day is: Monday (value of: 1)

or even on array (as Richard MacCutchan point me out to the original question):

string[] WeekDays = new string[]{ "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday" };

Console.WriteLine("Days of week:");
for(int i=0; i<WeekDays.Length; i++)
    Console.WriteLine("{0} - {1}", i, WeekDays[i]);
Console.WriteLine("Choose the day (corresponding number):");

string choosenDay = Console.ReadLine();
int givenDay = Int32.Parse(choosenDay);
int prevDay = givenDay-1<0 ? 6 : givenDay-1;
int nextDay = givenDay+1>6 ? 0 : givenDay+1;

Console.WriteLine("given day is: {0} (value of: {1})", WeekDays[givenDay], givenDay);
Console.WriteLine("prev day is: {0} (value of: {1})", WeekDays[prevDay], prevDay);
Console.WriteLine("next day is: {0} (value of: {1})", WeekDays[nextDay], nextDay);

Result:

Days of week:
0 - Sunday
1 - Monday
2 - Tuesday
3 - Wednesday
4 - Thursday
5 - Friday
6 - Saturday
Choose the day (corresponding number):
given day is: Tuesday (value of: 2)
prev day is: Monday (value of: 1)
next day is: Wednesday (value of: 3)