Context. Observed young stellar objects (YSOs) are used to study star formation and characterize star-forming regions. For this purpose, YSO candidate catalogs are compiled from various surveys, especially in the infrared (IR), and simple selection schemes in color-magnitude diagrams (CMDs) are often used to identify and classify YSOs.Aims. We propose a methodology for YSO classification through machine learning (ML) using Spitzer IR data. We detail our approach in order to ensure reproducibility and provide an in-depth example on how to efficiently apply ML to an astrophysical classification.Methods. We used feedforward artificial neural networks (ANNs) that use the four IRAC bands (3.6,  4.5,  5.8, and 8 μm) and the 24 μm MIPS band from Spitzer to classify point source objects into CI and CII YSO candidates or as contaminants. We focused on nearby (≲1 kpc) star-forming regions including Orion and NGC 2264, and assessed the generalization capacity of our network from one region to another.Results. We found that ANNs can be efficiently applied to YSO classification with a contained number of neurons (∼25). Knowledge gathered on one star-forming region has shown to be partly efficient for prediction in new regions. The best generalization capacity was achieved using a combination of several star-forming regions to train the network. Carefully rebalancing the training proportions was necessary to achieve good results. We observed that the predicted YSOs are mainly contaminated by under-constrained rare subclasses like Shocks and polycyclic aromatic hydrocarbons (PAHs), or by the vastly dominant other kinds of stars (mostly on the main sequence). We achieved above 90% and 97% recovery rate for CI and CII YSOs, respectively, with a precision above 80% and 90% for our most general results. We took advantage of the great flexibility of ANNs to define, for each object, an effective membership probability to each output class. Using a threshold in this probability was found to efficiently improve the classification results at a reasonable cost of object exclusion. With this additional selection, we reached 90% and 97% precision on CI and CII YSOs, respectively, for more than half of them. Our catalog of YSO candidates in Orion (365 CI, 2381 CII) and NGC 2264 (101 CI, 469 CII) predicted by our final ANN, along with the class membership probability for each object, is publicly available at the CDS.Conclusions. Compared to usual CMD selection schemes, ANNs provide a possibility to quantitatively study the properties and quality of the classification. Although some further improvement may be achieved by using more powerful ML methods, we established that the result quality depends mostly on the training set construction. Improvements in YSO identification with IR surveys using ML would require larger and more reliable training catalogs, either by taking advantage of current and future surveys from various facilities like VLA, ALMA, or Chandra, or by synthesizing such catalogs from simulations.