Rectification has its pros and cons. You can do it yourself, but you'd probably at least want to buy a book on it, if you don't want to pay for a professional astrologer.
I've got one: Laurie Efrein,
How to Rectify a Birth Chart (The Aquarian Press, 1987.) If it is not still in print, you could probably locate a copy through an Internet used book seller. (She feels the Placidus house system gives the most accurate results, BTW; but your experience my differ.)
I think you would first want to learn the basics of astrology if you don't have them down already, because you'd have to have a good grasp of planets in signs, houses, aspects, and rulerships of different phenomena. You would also want to know the different predictive methods: transits, progressions, solar arcs. (Some would say primary directions, as well, but I've not used this method.)
The very best thing is just to get a copy of your birth certificate from the recorder's office in your birth place: however, not all locales include the birth times. Usually there is a short form and a long form--ask for the latter. Or a hospital record.
Important events that happen around the same time for everyone, like high school graduation, are probably not ideal. More like, some kind of accident or illness, a major move, the start or ending of a significant relationship. Lib, it looks like you were born in Cuba. If you are not living there now, for example, your mother could probably give you the date of your move.
An Australian astrologer, Alice Portman (
www.aliceportman.com ) works with transits of Uranus. Uranus represents sudden change, so consider dates when something changed quickly in your life, in ways consistent with the meaning of the next house. Ideally, the date of the change gives you the house cusp. For example, your Uranus is in the 5th house, but you may have noted a change in issues relating to work, service, and health when it transited into your 6th house. An important new relationship beginning, an old one ending, or sudden changes in issues relating to enemies would be consistent with Uranus moving into the 7th house.
This is about the simplest method. Basically once you've nailed down some dates, look up Uranus in an ephemeris to see what degree and sign it was in.
Then you can do this with other planets and hypothetical angles, consistent with their meanings as they move into different houses by transit (slower moving planets) or progression (faster moving planets.) Some people find solar arcs to be very accurate (equate the movement of each planet or angle a day equivalent to a year of real life. For example, if you're 18, rotate each planet 18 degrees ahead to see where you're at now.) Thankfully the free charts at Astrodienst will do this all for you.
I don't know that this will ever be totally accurate, however. I didn't know my birth time when I first studied astrology. My mother had passed away, there was no baby book saved, &c. My birth certificate from the county recorder's office didn't include the time. A professional astrologer guessed my rising sign as Leo, on the basis of my appearance. My rectification efforts produced early Libra. When I finally found a copy of a different birth certificate from the suburb where my parents lived among her papers, I found a birth time. My ascendant turned out to be in late Virgo. I wasn't off by a lot of degrees, but it was enough to produce a sign change.
Can I see Virgo in myself now? Sure. But here's the kicker. My ascendant degree is closely squared by Uranus. So no way was I going to fit the neat and tidy stereotype. You have to allow for first house planets or close aspects to the ascendant giving off their own signals.
Lib, right now your ascendant choices appear to be Leo or Virgo. I would suggest you start working with them, in the first instance.
