In the various articles, they investigated the adsorption mechanism with different analyses such as FTIR, XPS, DFT, and SEM. Are there a special pattern? Are you have information about DFT?
The choice of method is always related to the information you want to gather.
Microscopic methods, especially AFM and STM [SEM maybe not so much] can tell you the final adsorption geometry and you can learn something about surface diffusion of adsorbates, going so far that you can track individual adatoms if your STM is capable of the Swartzentruber method. AFM and STM also allow for direct manipulation of the adsorbates.
FTIR is generally not very surface sensitive, but there are selected adsorbates for which it can be used reasonably, especially CO and water. For CO you can deduce directly from the shift of the carbonyl band whether the C-O-bond has been stregthened or weakened thus also differentiating chemisorption and physisorption.
XPS tells you something about the change in the bonding situation of individual atoms by assigning characteristic chemical shifts to certain bonding situations. Unless there is already strong literature on your system, XPS can't be evaluated standalone but needs theoretical support, usually from DFT.
DFT is still the running horse of quantum chemistry since it gives the best results on the N4 scaling calculation level (N3 if your software can do RI). You can do supporting calculations for all previously mentioned experimental methods and also calculate transition states for all sorts of processes. Please note that surface calculations are pretty hard to do and also costly, so be sure you have someone around from whom you can personal help with it.
I'm going to add TPD, temperature programmed desorption, to the mix which allows for measuring the desorption activation energy which can be used as an approximation for the adsorption energy and of course that tells you a lot about the nature of the bond. TPD also allows to measure lateral interaction energies and desorption kinetics orders.
On what level do you need info? Do you have any previous education on quantum chemistry?
If not, then Jensen's "Introduction to computational chemistry" followed by Burke's "ABC of DFT" would be good starters.
If it's about actual calculations, many program packages have tutorials as pdf or youtube videos. For that, you need to know which software you want to use and, as already posted above, if someone in your institute already has expertise with one, it's probably best to join.