How are the element abundances calculated for a meteorite in the Hydrogen log10 scale? In astronomy, solar abundances are often calculated or tabulated per $10^{12}$ H atoms. I understand that in case of the Sun this can be done because H atoms are in majority or are present for a scale comparision. 

How can the same element abundance be calculated for an example meteorite which does not have any volatile gas such as H? In particular, I am referring to the table 1 of http://astro.uni-tuebingen.de/~rauch/TMAP/grevessesauval2001.pdf. It lists Solar abundance and lists meteorites abundance as a comparision. How have they calculated the element abundance for a meteorite in the $log_{10} \epsilon_{H} = 12$ scale?

Finally, I have a sample rock which has its's composition given in Weight $\%$ of various oxides such as $SiO_{2}, MgO, FeO$ etc. I have to convert these into elemental abundances in $log_{10} \epsilon_{H} = 12$  scale. How should I do this?

Thanks in advance!
Meteorite abundances are referenced to their silicon abundance and then that is bootstrapped onto the hydrogen scale by assuming that the silicon abundance of meteorites is the same as that in the Sun. See for example Asplund et al. (2009). 
This means there is an additional uncertainty of a couple of hundredths of a dex when comparing meteoritic and solar photospheric abundances.

So the answer to your second question is work out the abundances relative to Si and then use the solar Si/H ratio to put them on the hydrogen scale.