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I'm struggling to find much information about yield curve interpolation for sub-yearly horizons. Say, one-two months. It seems to be the area where the curvature is usually nontrivial, while after that it's not that different from a straight line, oftentimes.
Is there some method quants use for this task by default, as a simple yet effective estimate? Some industry standard? Or if it's more complicated than that, what literature should I read to get a good overview of existing methodologies?
It depends on the market you're interested in and what the curve is used for.
To build the USD swap curve, for example, you've got a ton of information available from actively traded market instruments – fed funds futures (monthly), OIS (even finer details at the front end), Eurodollar futures (quarterly), basis swap, etc. All of these should be incorporated into your curve building procedure. A lot of curve builders will fit most if not all of these available market instruments perfectly and simultaneously.
For the government curve, it's a different story. In the US, most curve builders are not particularly concerned about fitting the front end of the Treasury curve all that well. In fact, 1) most of us are likely to fit the <1y sector by itself as a separate curve, 2) some of us use repo rates rather than Treasuries at the front end, since this gives more accurate forward rates (Treasuries are financed at repo rates).
I assume that with 'yield curve' you mean US Treasury curve. The very short end is determined by the Fed rate, therefore one uses flat forward interpolation between Fed meeting dates (which are every 1.5 months). Same thing happens with OIS.
