Hi Erman, personally, I think that the easiest and quickest way predict catalytic activities of an unknown enzyme is to compare its amino acid sequence to other proteins using online tools such as BLAST or ExPASy.
Amino acid homology will give you a starting point for examining 3D models.
Unless you are lucky and find substrate(s) in the active site of the protein, it is difficult to determine the specific reaction catalyzed by the protein. What you may identify from the overall structure is the kind of reaction catalyzed...
As Steingrimur suggested already, an amino acid similarity search (BLASTp) should be your first port of call. Many BLAST tools will identify conserved domains and the description of the domains will give you a good idea of what reactions they generally catalyse.
If your structure is novel and a BLAST doesn't find statistically significant homologues, then try a 3D search (e.g. the DALI server) that will identify other structures with a similar fold regardless of their amino acid sequence. If you are a structural biologist or similar, you might be able to identify the possible active site/s and compare the residues in that area. If the potential catalytic residues are conserved and the activity of the structural homologue has been described, then this might give you a clue towards the activity of your enzyme.
In any case, you will need to test and prove any hypothetical activities you come up with ... speculations are generally hard to publish.
Shoichet's group (the one developing UCSF Dock) has some interesting papers on this subject. See this one for example: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17603473&query_hl=1&itool=pubmed_docsum
I agree with most of the other commenters that activities can be predicted by structural comparison to known enzymes. This relates to the follow-up question regarding the pathways the enzyme participates in. To correctly predict an enzyme's biological activity one must predict the biologically relevant reactants and products, as well as the functional context. Since those can't be directly encoded in the protein structure, one cannot assuredly predict a biologically relevant pathway, even if one can predict catalytic activities by homology.
Adding to the above: if you BLAST directly against a pathway resource such as KEGG...
http://www.genome.jp/tools/blast/
...you can get an idea of which pathways the most similar (or a few quite similar) enzymes act in directly from the results.
Also, in addition or instead of BLAST, run InterProScan on your sequence, which is a meta-resource querying about 10 other protein motif, domain, etc resources.
For structure-only based searching there are things like 3D-BLAST (a resource) and e.g. the I-TASSER suite of tools, there e.g. COFACTOR. Just google 'em!