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We present the methodology for a joint cosmological analysis of weakgravitational lensing from the fourth data release of the ESO Kilo-DegreeSurvey (KiDS-1000) and galaxy clustering from the partially overlapping BOSSand 2dFLenS surveys. Cross-correlations between galaxy positions andellipticities have been incorporated into the analysis, necessitating a hybridmodel of non-linear scales that blends perturbative and non-perturbativeapproaches, and an assessment of contributions by astrophysical effects. Allweak lensing signals are measured consistently via Fourier-space statisticsthat are insensitive to the survey mask and display low levels of mode mixing.The calibration of photometric redshift distributions and multiplicativegravitational shear bias has been updated, and a more complete tally ofresidual calibration uncertainties is propagated into the likelihood. Adedicated suite of more than 20000 mocks is used to assess the performance ofcovariance models and to quantify the impact of survey geometry and spatialvariations of survey depth on signals and their errors. The samplingdistributions for the likelihood and the $\chi^2$ goodness-of-fit statistichave been validated, with proposed changes to the number of degrees of freedom.Standard weak lensing point estimates on $S_8=\sigma_8\,(\Omega_{\rmm}/0.3)^{1/2}$ derived from its marginal posterior are easily misinterpreted tobe biased low, and an alternative estimator and associated credible intervalhave been proposed. Known systematic effects pertaining to weak lensingmodelling and inference are shown to bias $S_8$ by no more than 0.1 standarddeviations, with the caveat that no conclusive validation data exist for modelsof intrinsic galaxy alignments. Compared to the previous KiDS analyses, $S_8$constraints are expected to improve by 20% for weak lensing alone and by 29%for the joint analysis. [abridged]

KiDS-1000 Methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis