I would like some guidance in tracing the burial place for a person who died in Surrey, England in the 20th or 21st century.
In many way 20th and 21st century events are harder to track down than earlier events without visiting local record offices, because the focus of much work to put records online has been on the earlier events.
However, there are a number of steps you can take, but first a word of caution: Do not assume that somebody who died in Surrey was buried (or cremated) in Surrey. In my own family, there is an instance of a couple dying in the late 1940s/early 1950s in Birmingham, England who were buried in Merthyr Tydfil, Glamorgan. So, unless you have very good reason to be sure of a Surrey burial or cremation, keep an open mind and look further afield (in places where the family might have had connections) if you don't find him in Surrey.
Where exactly was the death registered/did the death take place? This may be a clue that helps narrow down where the burial might have taken place (subject to the caveat above). If you don't already have this information, Freebmd.org.uk may help, depending on date of death (their coverage for the 2nd half of the 20th century is very incomplete, and they have zero coverage for 21st century). Findmypast.co.uk and ancestry.co.uk have complete versions of the GRO death indexes up to 2006, but require a subscription (or a free trial account). The death certificate will be even more specific about the place of death. (For deaths before 1966, the National Probate Calendar may also help narrow down a location if he left a will -- ancestry.co.uk has it online.)
Is anything known about his residence in the period running up to his death? Again, this may help narrow down the possibilities.
ACproctor has already suggested (https://genealogy.stackexchange.com/a/3216/104) contacting the relevant local councils to search cemetery records of burials and cremations. Some records are online at deceasedonline.com, but not (I think) Surrey. There's a list of Surrey cemeteries and crematoriums at GenUKI.
You should also consider the possibility that he was buried in a churchyard, which may be Church of England or non-conformist or Roman Catholic or a burial ground associated with a synagogue, if he was Jewish. I can't locate any Surrey registers online, so you may have to trawl a lot of individual parishes, especially if the death is recent enough that the registers are still held by the relevant church/congregation. Note also, it isn't unknown for a "church burial" to take place in a "council cemetery" — I have an example in North Wales where the burial is recorded both in the parish register and the council records for the cemetery (just across the road from the church).
There may be an obituary or a brief death notice in a local newspaper, as suggested by PolyGeo at https://genealogy.stackexchange.com/a/3212/104. For very recent deaths (since 2007) http://www.bmdsonline.co.uk/ may help. For deaths before 1949, the British Newspaper Archive has some online coverage. Otherwise, you may need to visit a local history centre in Surrey to search.
When searching, bear in mind that the information available to whoever recorded the death, burial or cremation may not be accurate, depending on how well the person providing the information knew him. For example, age may be estimated, so don't search for exactly the right age or date of birth. Similarly, the name(s) (especially forename(s)) recorded may not match the name he was given at birth, or by which he was commonly referred to by his family, so look for combinations and variations, or even just initials.
How will you be sure you have the right burial/cremation? This is another point at which the death certificate is useful, especially if you're dealing with a common name. The death certificate will give place and date of death, and (possibly) usual address of the deceased. Either the place and date of death, or the usual address, should tie up with the burial records.
Contact the local council to find out if local cemetery records have been digitised, and so can be searched for a given name, or whether they can perform a search for you. I know of several councils that have done this although the level of support varies from fully-indexed text to mere scans that have to be read manually. The registers for some "active" cemeteries may not have been made available. I have come up against this before but do not really understand the rationale since records preceding some arbitrary date could still be digitised.