Hey Boston,
I have no idea how you're going to find straight photography jobs, although that I am sure that there are some here.
Try this to start: http://www.cv.lv/darba-sludinajumi/q-fotogr%C4%81fiju/
If you have a media/marketing focus, then you should look look for such work to start.
If you are certified or educated, then there is a better chance that you can get a job teaching English. There's a guy (who's name I've stupidly forgotten), also an American (I think) who was looking for people to hire for teaching. They will sponsor work permits.
It is possible to enter the country with a visitors permit (90 days) and then apply for a working residence permit, but it takes 30 days mininum to get a residence permit, so it depends on what you can afford (Americans can't officially work with a visitor permit.)
To recap, the process for an American to get a residence permit is:
1. Make sure that you are allowed to get a residence permit without a VISA (I am Canadian and I didn't need a VISA,)
2. get the forms on the immigration web site (http://www.pmlp.gov.lv/en/pakalpojumi/uzturesanas.html)
3. request an appointment at the pmlp office (sometimes a week delay or more - small town offices have much better lineups than Rīga)
3. present the forms, with additional requirements (get another appointment now);
4. return after 30 days or so to receive permit;
The requirements for the permit are:
1. reason for permit -> marriage info, or signed employment contract (in Latvian)
2. modest health insurance (most insurance office in LV offer a cheap product specifically for this purpose for $20 a year or so;)
3. pictures of you;
4. passport etc;
5. rental contract, or a letter from a domestic property owner saying that you are staying with them;
6. you must be in the country legally to receive your permit.
With regards to 6, you can actually violate that, if you're willing to pay a fine and have a violation on your travelling history in Europe.
Some suggestions:
1. especially if in Rīga, be nice to the receptionists at the PMLP office, and they will treat you well back. If they know that you don't speak LV/RU they will still try to help you. The actuall PMLP offices always have at least one English speaker working.
2. If you can go in with an LV speaker at the beginning, it is very helpful.
For Europeans reading this you don't have the same requirements, for Non-Europeans, you may need to also apply for a VISA.