If your relative does not have at least settled status then you will have to make do with either a visit visa for 6 months or apply as a dependent on their study or business visa etc. If they have at least settled status then you can either apply for a visit visa or marriage visit visa if staying less than 6 months, otherwise apply for a family visa. Family means carer, child, parent or partner. There is sometimes a possibility to extend or switch to a family visa, but not from a visit visa of under 6 months unless as a fiance(e). Home Office will want proof of money and English. It costs £1,523 for a normal family visa from outside the UK, plus the NHS surcharge. If your relative in the UK is here on a work or study visa you would apply as a dependant on their visa not on your own family visa. You need to tell Home Office about where your relatives have lived and travelled around the world, plus a TB test and clean criminal record. Family visas except marriage visas allow work and study.
English
You normally need English if you might need to work. There are exemptions for children, adults coming for care, over 65s, disability and partner/parent family visas being extended after 5 years. Acceptable qualifications include a degree taught in English, but you have to pay £180 for a Naric visa & nationality certificate if your degree was not in the UK; alternatively you can take a SELT test and achieve CEFR A1 in speaking and listening. When you extend after 2.5 years you may have to prove you have improved.
Maintenance
Couples or those looking to settle within 5 years need an income (eg salary or profit for 6 months, or rent, interest or pension) of £18,600, plus £3,800 for the first child and £2,400 per extra child who does not have at least settled status. You typically prove earning with bank statements, payslips and employer's letter. Without the minimum income requirement you might be able to apply under the 10 year route to settlement, or under the 5 year route as a parent.
Partner route
For a family visa as a partner you need to prove you are married, have cohabited for 2 years from application date or will marry within 6 months of arrival, and have English and maintenance. There are exemptions if you have a British child living in the UK for 7 years for whom it would be unreasonable to leave, there would be insurmountable very significant difficulties living with your partner in the home country or stopping you coming would breach your human rights. Partners can stay 2 years 9 months and fiance(e)s can stay 6 months before applying to switch to spouse route. Your non-independent under-18 children can be added as dependants. It can potentially be extended. After as little as 5 years as a partner you can apply for indefinite leave to remain. You need proof of relationship such as your story since meeting and joint bills.
Parent route
If you do not qualify for partner route to a family visa there is the parent route. This is based on your non-independent under-18 children living in the UK, for whom you have sole parental responsibility, or the other parent is not your partner and has at least settled status (unless they are from Europe or you are applying within the UK) and you have access rights. You must prove you help raise the child, eg with letters of support from school, doctor or the other parent. You need English and maintenance unless the child has lived in the UK for 7 years and it would be unreasonable for them to leave and usually they have to be British. It lasts 2 years 9 months and can potentially be extended or switched to for 2 years 6 months. You need proof of relationship and details about any other parent.
Child route
If your parent has permanent residence or indefinite leave to remain you can apply for settlement. Otherwise you can apply for a family visa to join your parent who has limited leave to remain. If you were born in the UK you get the same rights as your parent. In any event if you are under 18 you can apply on your own or be added as your parent's dependent. If you are over 18 you can only apply if you were under 18 when you got a family visa, live in the UK and are non-independent. Probably you were born outside the UK, in which case you must be under 18, someone must be maintaining you, you must be non-independent and must not be married, and you apply on the back of your parent's application for leave as your parent or your parent's partner; otherwise there is an exemption if there are serious reasons to give you leave and there are plans for your care. If you are over 18 you must be non-independent and had a family visa before you were 18; otherwise you might be able to apply under the private life 10 year route. You apply from the UK online or outside the UK on a form that depends what your parent is applying for.
Care route
You can apply for a family visa as an adult dependant relative, for long term care by a grandchild, child, parent or sibling, who lives permanently in the UK, who can afford to look after you for 5 years, when you cannot afford it in your home country and your sponsor cannot buy it for there either, and normally they need to have at least settled status. It lasts as long as your relative's leave and stay, so if they are have settled status you should never need to extend.
Private life
You can apply online relying on your private life human right if you live in the UK and are:
under 18 and it would be unreasonable to expect you to leave,
18-24 and lived in the UK continuously for half your life,
over 25 and have been in the UK for 20 years, or
over 18 and have been in the UK under 20 years but would have very significant problems being sent to another country.