The Importance of the Moment
It's almost an axiom of Astrology that you need an accurate timing before you can draw up a useful chart (and an accurate location). That's because, as Dave said, the birth time, together with the location, determines your Ascendant and that in turn determines the structure of the chart. It places the planets in the various houses, each of which has a significance for an area of your life. So, using a very simple example, a transit by Jupiter of a natal planet, usually is associated with good fortune or good things happening. However, without a chart, that's as far as you can go. Something good might well happen, but what it relates to you haven't really much of a clue without a chart.
If you're looking at a natal chart, the timing is taken for the moment of birth and often that is just not known, either at all, or is only known within several hours - for example, you know you were born in the morning, but not exactly when.
Obviously you could try and tie down your birth time to a more exact moment but that is often easier said than done. Alternatively you could 'think outside the box'. If you're interested in transits relating to your career, you might not know your birth time but you may well know a fairly accurate time for the moment you were appointed, or went into the interview. You can always set up a chart for that moment and examine it. It relates to one area of your life in more detail but if it is the area that you are interested in, that will work.
You could do the same for your marriage (assuming you were married) because you have a recorded time, date and place. You could do it for your home and family, if you have a time for signing the contract on your house/apartment.
The Astrologer, Geoffrey Cornelius has also shown that 'wrong' times can still lead to useful information, having analysed a chart based on an incorrect press release of the natal details for Princess Diana.
You can even construct a natal chart which assumes you were born at sunrise, or noon (assuming no better indication) and analyse that. Indeed the whole basis of those 'Your Stars' columns is that you were born at sunrise, and as they are not date specific (apart from the start and end dates, which themselves may be a day or so out) they deal in transits of your houses based on whole signs. So if you were born with the Sun in Taurus, Taurus becomes your first house, Gemini your second, Cancer your third, Leo your fourth and so on. All you need do is find where the planets are on the date you were interested in and this gives you their location by house. So Saturn in Sagittarius would be transiting your eighth house and that would suggest that your partner may have money problems, or the inheritance you were expecting is going to be less than you think it will be.
If you've read your 'Horoscope' column, you will know that occasionally it's right but more often it's wrong or so vague that you can't be sure. So clearly it's not a preferred method but it might be better than nothing.
Lastly, even if you do have a correct birth time, transits don't always seem to work. There used to be a belief that this was because transits were only useful when the planet was active, usually through a Direction, Progression or through a Time Lord. So a transit might be significant if it fits into what is promised in a Solar Return and is transiting one of the SR angles, otherwise it's possible you won't notice it. Most of those other methods requie a more accurate birth time than a guess.