In Roe v. Wade, the primary holding is that "a person may choose to have an abortion until a fetus becomes viable, based on the right to privacy contained in the Due Process Clause of the Fourteenth Amendment. Viability means the ability to live outside the womb, which usually happens between 24 and 28 weeks after conception". The opinion finds that there does exist a right to privacy, and that it is protected by the First, Fourth, Fifth, Ninth, and Fourteenth Amendments. It is immaterial that there is no mention of abortion in The Constitution. There is also no mention of TV and radio transmissions, the internet, speech-amplifying devices, or automated forms of text reproduction and yet the vague words of the First Amendment w.r.t. "press" and "speech" are interpreted as protecting your right to blog. Revolvers and various other firearms that did not exist at the time of the writing of the constitution are not mentioned, but they (the right to have them) are protected under the Second Amendment. Lack of specific mention is irrelevant to determining constitutional protection.
§VIII of the opinion discusses the right of privacy, and the ruling roots the recognition of that right in Union Pacific R. Co. v. Botsford, 141 U. S. 250, and numerous other SCOTUS rulings – Stanley v. Georgia, 394 US 557; Terry v. Ohio; Katz v. US, 389 US 347; Boyd v. US, 116 US 616, Olmstead v. US, 277 US 438; Griswold v. Connecticut, Meyer v. Nebraska, 262 U. S. 390 and so on.
You might then look at the Dobbs ruling to see whether those arguments are addressed and refuted. That, at least, is where you would start in understanding the legal background.