In this chapter, Moses repeats the commands about clean and unclean animals and establishes two new tithes (or is it just one?).
"You are the children of the LORD your God" (v. 1). Although it hasn't been mentioned much, the LORD will increasingly be expressed as a father figure to the nation of Israel. I don't remember if this is the first verse to state it in such explicit terms, but I know that earlier in the Pentateuch the LORD has been primarily depicted as a lord or suzerain. These should not be considered mutually exclusive positions. Father/son terminology generally indicates a friendly relationship (source). The earlier language depicts the LORD as powerful and beneficent to Israel, but father/son language also conveys an emotional connection because it is generally assumed in the bible that fathers love their sons.
We also see the LORD expressing love for Israel more and more (e.g. Deut 4:37, 7:7-8, 7:13, etc.). Sonship is probably more important because it also implies love, but also inheritance and everything that goes with it. The LORD will never die, but it is nevertheless implied that the sons of God would inherit, in whole or in part, the dominion of God. This began in Gen 1:28-29 with the assignment of the earth to man. When the LORD calls Israel his son, we can infer that the process was not ruined by sin, though certainly it was delayed.
In the future, we will see father/son language appear with much greater frequency.
Verses 2-21 are largely copied from earlier chapters. Verse 2 is taken from Lev 19:27. The section on unclean animals is taken from Lev 11. The command against boiling a goat in its mother's milk is repeated in Ex 23:19 and Ex 34:26. I don't feel any need to discuss these parts because they are nearly identical to the prior passages on the same topics.
The last part of the chapter (verse 22 to the end) is far more interesting because it creates a new tithe or two. First, recall that there was a tithe established earlier in Num 18 for the provision of the Levites and priests. That tithe was " reckoned ... as the product of the threshing floor, and as the product of the wine vat", which implies it is only taken from agricultural produce. It is not stated if this tithe should also include animals or other kinds of produce, though I do think the language is meant to be expansive and not restricting (i.e. probably meant to include other kinds of produce and maybe also animals).
Here, the tithe is established not to sustain the religious orders or the temple, but rather was to be brought to the LORD's dwelling place and eaten there by the people offering it. More specifically, we see that the tithe was only taken from grain, wine and oil (i.e. agricultural produce). The animals are not tithed, but the Israelites must offer the firstborn, which has been previously stipulated (among other places, Ex 13). Because the animals are not tithed, I think we can reasonably question whether the tithe in Num 18 included animals. Also remember that the Levites are given a pastureland around their cities, which suggests they would raise their own animals, though it could be those animals were tithed.
As in Deut 12:21, there is an obvious expectation that some Israelites will settle far away from "the place which the LORD your God chooses", and in this case Moses creates a provision for the Israelites exchanging their goods for money to bring to the new temple and celebrate there.
In verse 28, we have a reference to another tithe being given in the third year for the sustenance of the Levite, foreigner, orphan and widow. Based on the way this tithe is phrased, I think it is not meant to be a separate tithe on top of the tithe from v. 22. I think it is more likely that this means every three years the Israelites take their tithe and give it away, rather than bring it to the temple and celebrate there. That is, in the third year would the people pay a single* tithe towards the poor or two tithes, one given to the poor and a second taken to the temple to celebrate? I contend that there is only a single tithe in this year. Keil and Delitzsch agree with this interpretation, but there is understandably confusion around this point.
The reasons why I think v. 28-29 describe an additional condition to the prior tithe: 1) it is part of the same chapter and same discourse, 2) it doesn't have the same boilerplate language about what must be given in the tithe (in v. 22-23), 3) v. 28 seems to reference the prior tithe, calling it "the tithe of your produce in that year".
Overall, there is a larger question of tithing in the modern church, and while I'm tempted to write a long discourse on that subject, I think it would be more appropriate to reflect upon it later, in the context of the NT. Certainly this chapter and Num 18 give us much-needed context on this modern question.
*"Single" only in the context of this chapter. In practice, there are at least two tithes (the aforementioned tithe to the Levites from Num 18), but probably even more since in later Israelite history the kings would also demand tithes (for instance, see 1 Sam 8:15-17). So we can expect there were at least three separate tithes, possibly four.