The artefacts of the Mishkan were not transported as is. They had to be carefully covered, following very specific procedures, as the artefacts were Holy and could not have been touched just by anybody.
Details of the packing procedures of the artefacts of the Mishkan, as well as the Mishkan parts itself, are outlined in the Book of Numbers(Bemidbar) 4:1-6. The description starts with the procedures for the Ark Of the Covenant, so let's take a look:
1 And the LORD spake unto Moses and unto Aaron, saying,
2 Take the sum of the sons of Kohath from among the sons of Levi, after their families, by the house of their fathers,
3 From thirty years old and upward even until fifty years old, all that enter into the host, to do the work in the tabernacle of the congregation.
4 This shall be the service of the sons of Kohath in the tabernacle of the congregation, about the most holy things:
5 And when the camp setteth forward, Aaron shall come, and his sons, and they shall take down the covering vail, and cover the ark of testimony with it:
6 And shall put thereon the covering of badgers' skins, and shall spread over it a cloth wholly of blue, and shall put in the staves thereof.
1 וַיְדַבֵּ֣ר יְהוָ֔ה אֶל־מֹשֶׁ֥ה וְאֶֽל־אַהֲרֹ֖ן לֵאמֹֽר׃
2 נָשֹׂ֗א אֶת־רֹאשׁ֙ בְּנֵ֣י קְהָ֔ת מִתּ֖וֹךְ בְּנֵ֣י לֵוִ֑י לְמִשְׁפְּחֹתָ֖ם לְבֵ֥ית אֲבֹתָֽם׃
3 מִבֶּ֨ן שְׁלֹשִׁ֤ים שָׁנָה֙ וָמַ֔עְלָה וְעַ֖ד בֶּן־חֲמִשִּׁ֣ים שָׁנָ֑ה כָּל־בָּא֙ לַצָּבָ֔א לַעֲשׂ֥וֹת מְלָאכָ֖ה בְּאֹ֥הֶל מוֹעֵֽד׃
4 זֹ֛את עֲבֹדַ֥ת בְּנֵי־קְהָ֖ת בְּאֹ֣הֶל מוֹעֵ֑ד קֹ֖דֶשׁ הַקֳּדָשִֽׁים׃
5 וּבָ֨א אַהֲרֹ֤ן וּבָנָיו֙ בִּנְסֹ֣עַ הַֽמַּחֲנֶ֔ה וְהוֹרִ֕דוּ אֵ֖ת פָּרֹ֣כֶת הַמָּסָ֑ךְ וְכִ֨סּוּ־בָ֔הּ אֵ֖ת אֲרֹ֥ן הָעֵדֻֽת׃
6 וְנָתְנ֣וּ עָלָ֗יו כְּסוּי֙ ע֣וֹר תַּ֔חַשׁ וּפָרְשׂ֧וּ בֶֽגֶד־כְּלִ֛יל תְּכֵ֖לֶת מִלְמָ֑עְלָה וְשָׂמ֖וּ בַּדָּֽיו׃
First and foremost, per Num. 4:1-4, all of the artefacts of the Mishkan were transported by the family of Kohathites from the Tribe of Levi. However, Kohathites were only responsible for just the transportation of the completely covered artefacts. In fact, here is what is written in Numbers 4:15 and Numbers 4:17-20:
15 And when Aaron and his sons have made an end of covering the sanctuary, and all the vessels of the sanctuary, as the camp is to set forward; after that, the sons of Kohath shall come to bear it: but they shall not touch any holy thing, lest they die. These things are the burden of the sons of Kohath in the tabernacle of the congregation.
17 And the LORD spake unto Moses and unto Aaron saying,
18 Cut ye not off the tribe of the families of the Kohathites from among the Levites:
19 But thus do unto them, that they may live, and not die, when they approach unto the most holy things: Aaron and his sons shall go in, and appoint them every one to his service and to his burden:
20 But they shall not go in to see when the holy things are covered, lest they die.
15 וְכִלָּ֣ה אַֽהֲרֹן־וּ֠בָנָיו לְכַסֹּ֨ת אֶת־הַקֹּ֜דֶשׁ וְאֶת־כָּל־כְּלֵ֣י הַקֹּדֶשׁ֮ בִּנְסֹ֣עַ הַֽמַּחֲנֶה֒ וְאַחֲרֵי־כֵ֗ן יָבֹ֤אוּ בְנֵי־קְהָת֙ לָשֵׂ֔את וְלֹֽא־יִגְּע֥וּ אֶל־הַקֹּ֖דֶשׁ וָמֵ֑תוּ אֵ֛לֶּה מַשָּׂ֥א בְנֵֽי־קְהָ֖ת בְּאֹ֥הֶל מוֹעֵֽד׃
17 וַיְדַבֵּ֣ר יְהוָ֔ה אֶל־מֹשֶׁ֥ה וְאֶֽל־אַהֲרֹ֖ן לֵאמֹֽר׃
18 אַל־תַּכְרִ֕יתוּ אֶת־שֵׁ֖בֶט מִשְׁפְּחֹ֣ת הַקְּהָתִ֑י מִתּ֖וֹךְ הַלְוִיִּֽם׃
19 וְזֹ֣את׀ עֲשׂ֣וּ לָהֶ֗ם וְחָיוּ֙ וְלֹ֣א יָמֻ֔תוּ בְּגִשְׁתָּ֖ם אֶת־קֹ֣דֶשׁ הַקֳּדָשִׁ֑ים אַהֲרֹ֤ן וּבָנָיו֙ יָבֹ֔אוּ וְשָׂמ֣וּ אוֹתָ֗ם אִ֥ישׁ אִ֛ישׁ עַל־עֲבֹדָת֖וֹ וְאֶל־מַשָּׂאֽוֹ׃
20 וְלֹא־יָבֹ֧אוּ לִרְא֛וֹת כְּבַלַּ֥ע אֶת־הַקֹּ֖דֶשׁ וָמֵֽתוּ׃ פ
Therefore, it were the Priests who would be required to cover all of the artefacts of the Mishkan, especially those inside the Tent of The Mishkan. Let's take a look at how it was done: here is the Tent of the Mishkan...
The Priests would enter the Tent of the Mishkan to begin covering the artefacts. The process would begin by taking down the Inner Curtain(The Veil) that separated the Holy of Holies section of the Tent from the reset of the Tent.
The Priests would get on the ladders so that they can unhook the Vail from the Four Inner Pillars, and also to remove the Connecting Rods that connected the Pillars, and from which the Vail hung from.
However, the Inner Curtain(Vail) would not be just simply removed. The Priests would carefully unhook and lower the Vail down, without looking inside the Holy of Holies and at The Ark. Then, by putting the Vail on their shoulders and walking backwards, they would spread the Vail over the Ark.
The procedure of covering of the Ark with the Vail is similar in execution to the incident outlined in the Book of Genesis 9:23
23 And Shem and Japheth took a garment, and laid it upon both their shoulders, and went backward, and covered the nakedness of their father; and their faces were backward, and they saw not their father's nakedness.
23 וַיִּקַּח֩ שֵׁ֨ם וָיֶ֜פֶת אֶת־הַשִּׂמְלָ֗ה וַיָּשִׂ֙ימוּ֙ עַל־שְׁכֶ֣ם שְׁנֵיהֶ֔ם וַיֵּֽלְכוּ֙ אֲחֹ֣רַנִּ֔ית וַיְכַסּ֕וּ אֵ֖ת עֶרְוַ֣ת אֲבִיהֶ֑ם וּפְנֵיהֶם֙ אֲחֹ֣רַנִּ֔ית וְעֶרְוַ֥ת אֲבִיהֶ֖ם לֹ֥א רָאֽוּ׃
Therefore, in a similar manner, the Priests would cover the Ark of The Covenant with its first Covering. Here is a better view upon the Priest walking backwards with the Vail:
Therefore, the First Covering of the Ark of the Covenant was essentially the Inner Curtain (The Vail), ten(10) by ten(10) cubits in measurements. Here is what it would looked like:
And here is the view upon the covered Ark of The Covenant from the Holy Place, so that you can have a better idea of what it would looked like:
Once the Ark was hidden from the view, the other Coverings were placed over the Ark. The Second Covering, that was similar in dimensions to the Vail, was a square Covering of Tahash Skins.
This Covering was made of the same material as the Fourth Covering(Top Covering) of the Tent, and provided an extra protection for the Ark and for the covering Vail from the desert weather. Here is what it would look like, once it was placed over the Ark and over its Ark's First Covering:
The last Covering that was required to be put upon the Ark of the Covenant was a Blue Cloth Covering.
Similar in its measurement to the first two Coverings, this Third Covering served only one purpose: to make the covered Ark easy to spot and clearly visible during the transport in the desert.
Once all three(3) Coverings were spread over the Ark, they would have to be secured, so that they would not fall off during the transport. This was accomplished by "tucking" all of the Coverings between the short sides of the Ark and its carrying poles, as there was roughly a fingerbreadth(1cm) gap. Here is the rendering, of one of the side of the Ark, so that you can understand the concept:
The Exodus 25:15 states:
15 The staves shall be in the rings of the ark: they shall not be taken from it.
15 בְּטַבְּעֹת֙ הָאָרֹ֔ן יִהְי֖וּ הַבַּדִּ֑ים לֹ֥א יָסֻ֖רוּ מִמֶּֽנּוּ׃
Therefore, in order to keep follow this restriction, when the Coverings were "tucked" around the short sides of the Ark, the Carrying Poles were pulled out a little bit (just out of one pair of the Rings) and then put right back in and onto their places just like the last part of the Num. 4:6 says.
The resulting covered and ready to be transported Ark, with all of three(3) Coverings "tucked" and secured, looked like this:
And here is the view from a different angle (from inside the Holy Place of the Tent, so that you can see it better:
And when the four(4) Kohathites would carry the covered Ark of the Covenant, it would look like this: