How to cite my own submitted but not yet published work?
In principle you can cite other, submitted work in a research paper. Just give the authors, paper title, and either "Submitted." or "Submitted to [venue]." in the reference list.
However, both as a reviewer and reader, I usually find this disappointing. I already came across several cases where I wasn't able to find the cited paper even years after publication of the paper with the citation. It is well possible that the cited paper is rejected, and maybe someone just doesn't follow up to really get it published. As a better alternative, check whether you can put a preprint version of the paper you want to cite online (e.g. on arxiv), and just cite that.
You are allowed to cite works in submission as part of your ongoing research; this is something I've had to do on a number of instances for publications I wrote both in graduate school and as a post-doc.
The key here is that you must cite the work only as "Submitted to Conference A" rather than a standard reference to a work published in the proceedings. You would then, if possible, provide the conference paper A as an appendix or supporting information for the referees.
Citing something that is not published will prevent reviewers from doing their job, so it's a big no-no if you want to improve your chances of being accepted. The best way to go is to be patient and submit to B next year, having had the chance to improve using the reviews from A.
If this is not at all possible, you may be able publish A right now as a technical report from your lab/department an cite it as such. You'll have to check the guidelines of both conferences, namely if A accepts material previously published as a TR (in CS at least this is very common) and if B accepts citing TRs (usually also true in CS as long as it is easily available online).
Most importantly, when citing from a non-refereed source like a TR, you have to be very prudent in the way you characterize the work. Remember that it was only accepted in your department as an interesting document, not properly validated using the scientific contribution standards of your community. If I read a claim that something was "proven", or "shown", or "demonstrated" by a tech report, I'll probably reject the paper.
In any case, do not just cite A unless it is tangential (and in that case, why cite it all?). If it's actually important, give it an overview in your B submission, sufficient for a reviewer to keep on reading.