One of the perks of birding/watching is coming across a rare species. It is, by definition, a rare event. You can never predict it. You can help narrow down the chances of it happening to you by picking your birding arena carefully, and targeting the spring and autumn during helpful weather conditions. But even then you are not guaranteed anything.
I'm not one of those birders who has regularly found rarities. When I was particularly active in the late 70s and 1980s I reckoned on getting between one-three mentions in the BB rarities round-up (and 90% of these would have been 'commoner' rarities). Since then my appearance in that publication has been as regular as Lord Lucan's (before anybody points it out, I am aware that you actually need to go out birding to find something in the first place).
I was always interested in the type of birder who got the goodies - they were not always the ones that you would expect. It would be a fair assumption to make that a highly knowledgable ornithologist who spent a great deal of time in the field would score highly in 'finding rarities', but this is not always the case. I've known some exceptional birders who are just plain unlucky. They have put the time in, they know the score, but just happen to not be in the right place at the right time.
When I used to hang around observatories and reserves (in unhealthy amounts of time) I was struck by how little, proportionately, the staff actually found compared to irregular day trippers. Why was that? Did the resident observers walk around with complacency as a companion whilst the day-trippers were fresh and alert? Did the latter also look in places that the regulars shunned? I've seen this happen quite a few times where 'that rubbish gulley' or the 'crappy scrub' that never provided birds (and was subsequently shunned) played host to a rarity found by a birder who was unaware that that particular place was meant to be rubbish for birds.
I've known fairly average birders, whose appearance in the field might be best described as erratic, find a ridiculously high number of good birds for the effort expended. Maybe this sort of birder has exceptional eyesight or an almost supernatural ability to home in on rarity.
Most of the good birds that have come my way have actually come and found me. They have jumped out on a path as I've been ambling along; called overhead to get my attention; sang their presence from deep in a bush. Rarely have I gone out specifically on the hunt and come back rewarded.
But, I still maintain that time out in the field is the real 'must have' ingredient if you want to 'find your own'. It doesn't matter where you bird (rarity is relative). As long as you keep alert and put the time in you will be rewarded. And one last thing you will need - a big dollop of luck.