Wijnen.
IIRC in Standard Dutch it would be pronounced something like “vaynen”, but the v-sound would be a little softer than an English v-sound.
the ij combination is one letter, pronounced like the English long i. Maybe a good approximation would be veyenan with the v being a sort of voiced f.
No, I think that’s wrong. I took two units of independent study Dutch in college, and I was taught that “ij” is more like “ey” in English. Maybe it’s sort of in between the two.
Would the double i (as in “Liisa”) be pronounced differently than what we’d associate in English?
suits me. Rendering sounds from one language into the sounds of another is chancy. They rarely are an exact match.
My German friends used to rag each other about who had the best “th” sound, as in a wife telling a husband after he points out a mistake, “My th is better than yours.” None of them had it quite right and some of them still don’t even after 40 years. I’m quite sure I could have stayed in France after WWII and still not be able to get the French “eu” as in “feu” quite right.
There are a LOT of Dutch dialects. When I was in Belgium, (Brabant), the “ij” combination was sounded like a modified ee sound in English (so that we called the Dijle River, running through Leuven, the Dirty Deal).
However, if I were to pick the sound that was most prevalent throughout my travels in the Netherlands (and a few places in Belgium), I’d have said that “ij” was closest to the English long “i”, so that I’d have expected someone from Amsterdam or Maatricht to pronounce lijk similar to the English “like,” (with just a bit of a glide to it).
“Throatwarbler Mangrove”
Oh c’mon, you were thinking it.
I, for one, would not know what sound “ey” represents in English. I think **David **has the more correct answer, with the usual caveat about English dipthongs.
van Dijk = Van Dyke
I meant ‘ey’ like in ‘they’. True, we do say van Dijk (“Dike”) and Rembrandt van Rijn (“Rhine”), but I’d say that’s as much a result of Anglicized pronunciation, based on the English versions of both those words (“dike” and “rhine”), which happen to be close cognates. Anthony van Dyke the painter, moreover, spent a good part of his career in England; and the pronunciation of a name is usually not a good guide, especially when it is the name of a continental European who has emigrated to an English speaking country. It’s sort of like the case of the German born composer Handel–most people have probably been calling him “Handle” ever since he established himself in England, and only the most carping pedant would insist on the proper German pronunciation of the name.
I sort of agree with Tomndeb-- in most of “Holland” “dijk” would be close to “Dyck” except with an odd long ‘a’ sound before it-- like maybe further forward in the mouth. Like a fast ‘ay-ie’ dipthong? The Brabantines a more straight “deek”, and further west all hell breaks loose until you’re sure the people in Bruges are speaking some completely different language.
(not Dutch but studied it for a tad in Amsterdam and Antwerp and lived a year in Ghent, so grain of salt)
BTW, Tomndeb, KUL sucks! RUG rocks! (har)
edited to add-- looks like Spectre more or less agrees as well.
Native Dutch speaker here. I have never heard anyone pronouncing “ij” as “ey” in the way the English pronounce “they”. I think in the Middle Ages “ij” may have been pronounced as “ee” (as in “been”), but I’ve never heard Rembrandt van Rijn as anything other than “Rhine” (if you’re English you’re likely to mispronounce the “van”-part, but not the "Rijn"part). “Lijk” is pronounced as “like” when it refers to a dead body, but when it’s the last four letters of a longer word it’s usually more like “luck” (so, as an example, the word “pijnlijk” becomes “pine-luck”).
Pronounce “Wijnen” as a combination of the two English words “wine-an” with emphasis on the “wine” part.
How do you pronounce it? To me “Handle” seems as close as you can reasonably expect from a non-native speaker. Probably it sounds a bit too “English” but everything is within the right phonemes.
I think Händel is pronounced as the Dutch usually mispronounce the English word “handle”, that is, as “hendel”
Thanks 4.66! 
And is the double-I pretty straightforward?
I grew up in Michigan and live in Ohio: I could not care less about THE BIG ONE (the annual UoM/OSU season-ending football game).
I have one brother who is a UoM alumnus and one brother who is an MSU alumnus and I have no interest in that rivalry (and have never heard either one of them voice an opinion on the topic in the 30+ years since they were attending those schools).
I’m afraid that you picked exactly the wrong person to worry about some petty European scholastic/sports rivalry–my apathy appears to be genetic.
This says ij is a diphthong pronounced the same as “ei,” i.e. like the -ey in they. But this does not contradict 4.66’s data:
Look carefully at the vowel charts in that article. The monophthong open E sound is middle height (or “open-mid”). But when it’s diphthongized as “ei” or “ij”, it starts lower down, i.e. more open, more like /a/. The beginning of “ij” is a sound somewhere in between /E/ and /a/. This probably explains why it’s so hard to define for English speakers. It starts open (low) and moves toward close (high). In the corresponding English diphthong, it isn’t lowered at the beginning.
As for “w,” it’s… umm… I guess it depends on whom you ask:
“The realization of the /ʋ/ varies considerably from the Northern to the Southern and Belgium dialects of the Dutch language. In the South, including Belgium, it is sometimes realized as [w]. Some, mainly Hollandic, dialects nearly pronounce it like [v].”
So, “ee” = “i”, as in “bin”? 
IME, being the son of an immigrant, I’d go with 4.66.