If you guys want to give it your all and try to increase every possible chance of conceiving I suggest first reading the book Taking Charge of your Fertility. It's worth buying and is only about 20-30$.
Beige is 100% right on everything she's said but I will add to that and give you a few 'tasks' you both can partake to figure out when the ideal time is to basically have sex. THere's no pretty way of saying it, we refer to it as "BD" here, baby dancing.
Here are a few questions for you to figure out.
Are you wife's cycles regular?
How long are her cycles?
As beige stated, your wife should ideally ovulate between 12-16 days (generally it is 14 days. This is actually called the luteal phase or LP) prior to the first day of her period. The day of her period is considered as cycle day 1, or CD1.
So, if a woman has a 28 day cycle.
LP = 28-(12-16 LP)
LP = CD 12-16.
This is just an example, but if her cycles are 28 days, you should concentrate your BD efforts around those days, CD 12-16.
Now, there is a more full proof way to know when she will ovulate. There are 2 methods which I currently use. It will also determine what her luteal phase is and this portion of her cycle should never change by more then a day or so. This is the only consistent portion of a cycle. Once you know what the luteal phase is you can pretty much take a good guess at when her period would be due. For example, I know that from the day I ovulate, I will have my period in 12 days exactly and it is always bang on. 12 days is my LP. Anything less then 10 days is called a luteal phase defect however can easily be corrected.
The following are the two methods I spoke of:
One is an OPK (ovulation predictor kit). It's pretty much self explanatory. You pee on a stick, if it's positive, expect to ovulate within 12-36 hours. This means you need to BD it asap, and the day following too.
The other method is to chart her basal body temperature (bbt). This is very simple, and there is a very useful site online but per rules I can't post it. I suggest searching REMOVED. I found it very quickly that way. (sorry it's the best I can do). The book I referenced above also explains charting in a way I never could. As I said, this book is very valuable!!
Basically all she needs to do is buy a regular thermometer, nothing fancy is required. Every morning before she does anything, even before she stands up, as she's laying there, take her temperature and generally around the same time, it has to be after 3-4 hours of consistent sleep though if she was up earlier I'd suggest to take the temp both time and compare.
Every day, she can chart different types of signs like cervical mucous. I know it sounds wonderful but truely in the end, these things will help to pinpoint when your wife has ovulated. Generally they say a few months charting you can figure out your cycle (truely what you want to know is cycle length and luteal phase length) and then charting is no longer required. This can also be useful though to confirm you've BD'd at the right times (before using it as a reference tool). I can give you more info on this if you require it but thought I'd just give you a bit to start with.
One other thing I wondered about, since the doc said it's now or never. Have you gone for a sperm analysis? I know it sounds fun, but, if this is your only chance to conceive, I'd think that this would be very important in case changes in your diet are required or if you should try supplements/meds to help your swimmer if there are any issues. I'm not saying there are. In general, fertility issues occur more so in women then men since women's reproductive system is so much more complex.
Also, one other suggestion. Don't have sex every day. This can reduce your count as you're constantly having to replenish. I suggest every other day, or 3rd day once her period is done. Then, when you get around CD10 (10 days after her first day of her period) to move to every other day and then around CD12-15 I would try every day. However, if you're using OPK's.. a lot less sex is needed
(I don't know anyone who could go that often!!) as I said above, when you get the positive OPK, you bd every day for at least 2 days, if not 3. And also the BD'ing you've done prior will count.
BTW, just to somewhat correct beige.. most sperm live up to only about 3 days however some swimmers can last more, up to 6 or 7 days. I've seen women get pregnant from having sex only 6 days before their ovulation, since they charted their BBT and did their OPK's it was confirmed this way.
If you want more info just holler. I've done too much research on this crap and have been at it since last May. I don't want to completely overload you and this is going to be a lot to digest so far so I don't want to bombard you with more.
I also want to give you some koodos for putting effort into TTC. It shows how important this is to you and I honnestly can say I have not seen another male on here. It's nice for a change to see that a man is willing to go the extra mile and research just as much as women. I'd love for my fiance to be so interested in the in's and out's of this, however, all he cares about is "are you pregnant yet" lol.
Anyway, good luck and I really hope that you guys can conceive quickly!!