Tiree, do you know which orchid you have?

Assuming it is a Phalaenopsis (moth orchid) Spritzhenry wrote a superb blog 'Awkward Orchids' which will give you all the info to get your orchid flowering again. And welcome to GoY by the way!

As far as Phalaenopsis goes, that is a great blog Tiree. I would however add one or two things; firstly at this time of year I would leave the spike/s on. They may just be entering a period of dormancy and could rebloom as the days draw out. If the old spike starts to go brown, that is the time to follow Spritz's advice about cutting the stems back. If the flowering spike produced several "branches" I find that they are more likely to produce a new spike sooner than a plant that produces a spike with no branches coming off of it.

As far as other readily available orchids go, here's a quick rundown:
Paphiopedilum orchids come in two different flowering habits - sequential or non-sequential flowering. That speaks for itself, but a new flower spike will usually form on a different crown to the last spike. I use the trick of moving it to cooler room too to get a new spike.
Dendrobium orchids in my experience almost always need a cold "blast" to rebloom. You will not get new blooms from old flower spikes, so cut them off when they're finished. They mostly tend to flower from new canes (but not always), so it may take a season before these will rebloom.
Cymbidium are strictly once a season bloomers, so follow the blog advice on these. They will need a cooler room to induce new spikes. Also, to get them to rebloom reliably, they need about 10ºc difference between day and night temperatures.
Cattleya? God knows! I can't get a rebloom for love nor money!!
There is one other "type" of orchid commonly sold over here - Cambria. This is a misnimoer which encompasses a great number of intergeneric hybrids from the Oncidium alliance. Very difficult to offer any help on these without a picture I'm afraid...

Hope this helps.