How do I ask my photographer for a partial refund if she was late on the day of the wedding?

Check the photos see if they did an awesome job. The may have gone the extra mile for you to make up for it. They may also give you more images than contracted. 

Please look trough the contract and see the terms and conditions, if there is none in the contract you could just say how you feel how important the time that the photographer missed.

Prior to asking for a refund, consider a few things. 

Yes, ask for a partial refund if:

- they missed a crucial moment

- caused you stress due to their lack of punctuality

- if it had a follow on effect on other events of the day

No, don't ask for a partial refund if:

- if they give a great collection of photos for your wedding day which captures the memories in its entirety

- they offered to stay back longer beyond the original agreement

- they offered other discount or a compensation through other means (printing / frames / etc)

Generally, a good photographer would proactively mention how they felt for being late and what they can do to compensate for it. 

Now, after considering the above, if you have decided to ask for a refund, mention it to them in a positive manner. If you go hard and heavy, they may go into a shell and disagree. It's best to have an honest and polite conversation and hear what they have to say. I would then follow it up with an email to make sure you have captured the face to face conversation. If the photographer doesn't align himself with your views, then do consider if the amount of refund you are asking for is worth the staining the entire wedding photo collection with that memory. 

If they behave in an unprofessional manner, definitely do leave a review and let the world know. 

Keep in mind, don't spoil your memories of the day because of this, it would be a real shame. :)

A great photographer should really offer a discount or offer an alternative benefit, without the Bride & Groom needing to ask them for it. It's their big day, and the couple already have enough on their plate without needing to worry about chasing up on what may not have worked out as planned. If the photographer doesn't offer first, sending them something brief and in writing (eg. an email) is probably best, perhaps within a few weeks following the wedding.

Matching the discount/added benefit, to what would equal the time lost is probably different to every couple. But again, a great photographer should already know what matters most to the Bride & Groom and if they missed significant events they should compensate accordingly (eg. extra printing, better quality printing, extra editing, or reduced fees)...

I guess it would depend on how her lateness affected your day.

Did she miss a crucial part of the ceremony? Was there unmittigating circumstances as to why she was late? Did she ring you to let you know how late she would be? You need to take all this into account when requesting a refund. 

Were the photographs that she supplied you with poor quality due to the fact that she was stressed from running late?

I would approach her in a non threatening way for a casual chat and discuss it in a civilised manner first before demanding any type of refund.

Her reasons may of been very valid for being late. But ultimately did it really cause an upset on the day?

That depends on how late she was and what she missed really.

There's 10 minutes late and then there's missing the start of a ceremony. I always (without fail) arrive early and then I'm not stressed and haven't caused any stress to the bride and groom.
If the photographer charged by the hour then that is pretty straight forward - if they missed a crucial part (ceremony) then it's more complicated.

If your photographer is professional (and nice - which is why you booked them in the first place) they should approach you first to make reparation by some sort of compensation either by way of money back or more likely a gift of some sort ie free print / canvas, pages in an album etc.

This depends on the quality of the photos. If they are beautiful then time is not relevant  If photography was about time, then photographers would charge a bride more if she was late.

If she missed out on the ceremony or a key part of the day then you do have a point. Perhaps the photographer could make you a small album at no charge.  Hope you sort it out quickly because it will prevent you from cherishing the memories you do have.