I'm having trouble with the minfi package, specifically the read.metharray.sheet function.

The missmethyl package vignette loads the sample sheet from minfiData package like so:

library(minfi)
library(minfiData)
baseDir <- system.file("extdata", package = "minfiData")
targets <- read.metharray.sheet(baseDir)

I wanted to try the missMethyl package on public data and the minfi vignette shows how to load public data from NCBI:

library(GEOquery)
getGEOSuppFiles("GSE68777") # Get this accession/experiment
untar("GSE68777/GSE68777_RAW.tar", exdir = "GSE68777/idat") # untar the files
head(list.files("GSE68777/idat", pattern = "idat")) # look at the .idat files
idatFiles <- list.files("GSE68777/idat", pattern = "idat.gz$", full = TRUE)
sapply(idatFiles, gunzip, overwrite = TRUE) # decompress the .gz .idat files

library(here)
my_path <- here("GSE68777/idat")
head(list.files(my_path))

[1] "GPL13534_450K_Manifest_header_Descriptions.xlsx.gz"    
[2] "GPL13534_HumanMethylation450_15017482_v.1.1.bpm.txt.gz"
[3] "GPL13534_HumanMethylation450_15017482_v.1.1.csv.gz"    
[4] "GPL13534_HumanMethylation450_15017482_v.1.2.bpm.gz"    
[5] "GSM1681154_5958091019_R03C02_Grn.idat"                 
[6] "GSM1681154_5958091019_R03C02_Red.idat" 

If I unzip the csv and try read.metharray.sheet() I get an error (code not shown) because it's not a sample sheet! For example the minfiData sample sheet looks like this:

But GPL13534_HumanMethylation450_15017482_v.1.1.csv looks like a manifest file:

None of the other files that came with GSE68777 look like a sample sheet.

If you search under "MethylationEPIC" on NCBI GEO (array that works with missMethyl package) you will see that the majority of datasets do not have a csv or txt files, and the three others I tried [GSE86829, GSE103502, GSE103505] although they had text files did not have sample sheets. So how does one get this information?

This question doesn't really have anything to do with minfi. There is a function in minfi that will use a file output by the Illumina software to read in your data, and it works, so long as you have that file. So there's no error!

The issue at hand is that people submit data to GEO, following the instructions from the curators, and for array-based methylation data, it appears that the curators don't require that the sample sheet be included. That's not an issue with any Bioconductor packages, so is really beyond the scope of this site.

As to your question, there are three obvious answers. You could either contact the person who submitted the data and ask them for the file (by definition their email is part of the submission). Or you could try to generate a minimal file that will work. Or you could just read the data in by hand.