As a first step, I propose that you cannot do both: "I would like to simulate what a linguist sort of does and figure out the grammar of the language", and "construct a grammar given (only) a corpus". Instead, I suggest you have to do two things, in this order: (1) Understand how a linguist figures out the grammar of a language and (2) Understand how a linguist figures out the grammar of a language with suboptimal data. The second task presupposes the ability to do the first thing, and just makes the job much harder. It is possible that you absolutely could not figure out the grammar of the language, for example if you only have reams of monolingual text and no or little clue what they are about. If you pick the right language and only impose the condition "I won't work with a native speaker of the language", then you might well be able to do it (for example, Whitney did not elicit data from a native speaker of Sanskrit).
In the case of Xhosa, it is maybe a little too easy: gather up all of the descriptive material on the language, and read it. There are already reference grammars of the language and copious sources. The same goes for Zulu, Sotho, Tswana – but not Khoekhoe or Lushootseed. For Xhosa (or any other language with a decent grammatical tradition), the conclusions are already systematized, so that you would be told what the phonemes are, what a noun class is, and what the noun class markers are. In live field work, you discover these facts somehow (a book could and probably should be written on that topic).
Perhaps then a compromise would be to rely only on texts and their translations, and not grammars. A dictionary of Xhosa already contains a certain amount of grammatical information, for example it analyzes verbs down to roots (which never appear as such), and it will encode information about what kind of word indoda is (not just a noun, but its noun class). You might be able to reconstruct the grammar if you have sentences containing indoda where you notice that those sentences also contain the word "man" in the English version, and other sentences contain amadoda and the English word "men". This is actually a somewhat standard exercise in introductory linguistics classes.
Assembling the corpus and corresponding English translation would be the biggest impediment. DO NOT USE GOOGLE TRANSLATE, unless you only want to learn how Google Translate works (or not) and don't care about the language.
Given the premise that your only materials are a text and an English translation, you could start today with a Bible translation:
Ekuqaleni, kungekadalwa, wayeselekho uLizwi. ULizwi lo wayekunye
noThixo, naye ngokwakhe enguThixo ≈ In the beginning was the Word, and
the Word was with God, and the Word was God.
Not calling on any other resources, I look for recurring pieces and correlations between the two texts, eventually (based on more text) concluding that uLizwi or ULizwi means either "God" or "Word", and noThixo or enguThixo means the other thing.
The next verse
Yena wayekunye noThixo kwasekuqalekeni. ≈ He was with God in the
beginning
makes me believe that noThixo or enguThixo means "God". Expanding the search a lot more, I figure out that the choice between uLizwi and ULizwi is conditioned by syntactic position (the first letter of any sentence is capitalized). elsewhere I encounter the forms UThixo which correlates with the English "(sent) from God", and bakaThixo correlating to English "children of God". This continues for weeks of analysis, and based on examples like uYohane, uKrestu, uMoya I discover a rule that you prefix u- to a proper name. Ultimately I have a first pass parsing of the text that has resulted in some factual generalizations, and this leads me to question whether my analysis A is correct, or perhaps B works as well.
One problem is that my analysis B could predict the possibility of a form lekaThiko, but the fact that I don't encounter the form in the corpus does not mean that the form does not exist in the language. I will also never be actually correct w.r.t. the actual language, since (unbeknownst to me) the spelling system omits contrastive features of pronunciation (tone). But you could at least use this method to gain some insight into the structure of the language. The bonus is that at the end of the project, you can check existing linguistic research to see how close you came.